5WERS. 


CHARLES  SCRIBNER  &  CO,, 
ITew  York. 


LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

GIF^T  OK 


, 
Received         ^£j£jr  .  i8g  7  . 

Accession  No.  fe  7j&  ty  J     .    Class  No. 


NATURAL  SERIES. 


AN 


INTRODUCTION 


"ARITHMETICAL  ANALYSIS," 


DESIGNED    FOR 


PR  1  M  AUjY..^g  1  1  OOLS, 


CONTAINING 


e,  anli  Blackboard  (Sfoerciscs. 


S.  A.  FELTER,  A.M., 


GRADUATE    OP   THE    STATE   NORMAL   SCHOOL,   AND   AUTHOR   OP   THE   "  ARJTHMETICA1, 
ANALYSIS,"    "  PRACTICAL   PENMANSHIP,"    ETC. 


NEW   YORK: 

PUBLISHED   BY   CHARLES    SCRIBNER  &   CO. 

INGHAM  AND  BRAGG,   CLEVELAND,   OHIO. 

HADLEY,  HILL  &  CO.,  CHICAGO,  ILL. 


F.-f 


Entered  according  to  Act  of  Congress  in  the  year  18b3,  by 
S.   A.   FELTEB, 

In  th6  Clerk's  Office  of  the  District  Court  for  the  Southern  District  rf 
New  York. 


PREFACE. 


"  THE  favorable  reception  accorded  to  the  "Aritl* 
metical  Analysis,"  by  the  Teachers  of  the  Public 
Schools,  has  induced  the  author  to  prepare  this  little 
work  to  supply  a  want  not  reached  by  the  former 
book.  The  "Analysis"  is  intended  for  classes  com- 
mencing the  study  of  Written  Arithmetic;  this  book 
is  designed  for  those  commencing  the  study  of  num- 
bers,* and  is,  in  fact,  an  introduction  to  the  larger 
work.  • 

Teachers  of  the  ungraded  Public  Schools  are  often 
troubled  to  know  what  to  do  with  the  "little  ones," 

*  The  earlier  lessons  in  numbers  or  arithmetic  should  be  given  in 
connection  with  sensible  objects  and  not  from  books.  In  many  01 
our  best  schools  where  the  method  of  object-teaching  is  introduced, 
fessons  in  numbers  are  very  successfully  given,  and  all  the  elementary 
processes  of  arithmetic  are  taught  before  the  book  is  placed  in  the 
hands  of  the  pupil.  This  method  is  truly  in  accordance  with  the 
order  of  nature,  and  it  greatly  facilitates  the  future  progress  of  the 
learner,  while  it  charms  him  by  its  novelty.  This  system  of  instruc- 
tion by  objects  is  now  taught  in  the  N.  J.  State  Normal  and  Prepar- 
atory Schools  under  the  supervision  of  PROF.  WM.  F.  PHELPS.  This 
system  was  originally  introduced  into  this  country  in  the  Publio 
Softools  of  Oswego4  N.  Y.,  where  it  is  now  successfully  taught. 


IV  .  PREFACE. 

who  are  not  old  enough  to  spend  much  time  in 
study,  and,  consequently,  for  want  of  employment, 
uro*  annoyingly  mischievous,  or,  what  is  worse  for 
them,  listlessly  idle.  Many  teachers  within  a  few 
years  have  successfully  introduced  Mental  Arithme- 
tic as  an  interesting  and  profitable  employment  for 
this  class  of  pupils.  Many  others,  feeling  the  need 
of  a  greater  variety  of  exercises,  have  introduced, 
in  connection  with  mental  arithmetic  (as  far  as  it  is 
possible  to  do  so  without  the  aid  of  oooks,)  abstract 
operations  in  the  fundamental  rules,  thus  furnishing 
something  for  their  pupils  to  DO  while  they  are  of 
necessity  at  the  same  time  making  important,  advan- 
ces in  the  knowledge  of  Arithmetic.  These  teach- 
ers labor  under  great  disadvantages  by  being  obliged 
to  depend  entirely  upon  the  blackboard,  with  which 
few  schools  are  properly  supplied.  It  is  for  the 
purpose  of  supplying  this  want,  by  furnishing  a  co- 
pious supply  of  graded  exercises  both  mental  and 
written,  suitable  for  the  smallest  scholars,  that  this 
work  has  been  prepared.  The  following  are  some" 
of  its  peculiarities — 

1.  It  has  numerous  and  graded  notation  exercises 
for  reading  and  dictation,  without  rules,  thus  fol- 


PREFACE. 

towing  the  natural  method  of  instruction ,  facts,  first; 
principles,  afterward. 

2.  It  combines  mental  with  written  exercises  in 
such  a  manner  as  to  interest  by  constant  novelty. 

3.  The  Mental,  Written,  and  Blackboard  exercises 
are  copious  and   systematically  graded,  in  order  to 
place  difficulties  before  the  pupils  in  such  a  manner 
as  to  inspire  effort  rather  than  create  discouragement. 

4.  It  contains  mental  exercises  in  the  tables  of 
Denominate  Numbers,  with  numerous  review  ques- 
tions on  the  same. 

For  the  exclusive  use  of  the  teacher,  a  few  books* 
will  contain  answers  to  the  written  exercises,  but  in 
NO  CASE  should  they  be  placed  in  the  hands  of  pupils. 

If  this  little  work  shall  in  any  manner  aid  the 
Teacher  in  furnishing  something  for  his  primary 
pupils  to  DO,  and  thus  lighten  his  arduous  duties, 
the  author  will  have  been  abundantly  rewarded  for 
iiis  labor. 

COLLEGIATE  AND  POLYTECHNIC  INSTITUTE, 
BROOKLYN,  N.  Y.,  Feb.,  1863. 

*Copies  containing  the  answers  may  be  obtained  by  addressing  the 
publishers. 


PUBLISHER'S  NOTICE. 


WHEREVER  used,  FelterV  admirable  Text-books 
have  been  pronounced  by  practical  Teachers  to 
contain  the  most  perfect  system  of  arithmetical  in- 
struction published.  The  grading  of  the  books  is 
simple,  systematic,  and  complete,  and  peculiar  to 
the  series.  The  works  are  the  result  of  a  long  ex- 
perience and  service  in  the  school-room,  and  it  is 
believed  they  will  meet  the  requirements  of  every 
grade  of  schools. 

The  series  consists  of  the  following  books : 

Felter's  First  Lessons  in  Arithmetic,    (illustrated.) 

Felter's  Primary  Arithmetic,    (illustrated.) 

Felter's  Intermediate  Arithmetic. 

Felter's  Grammar-School  Arithmetic. 

Felter's  Intellectual  Arithmetic. 

Felter's  High-School  Arithmetic.*    (in  preparation.) 

FOR  TEACHEES. 

Felter's  Manual  of  Instruction. 

FELTEK'S  FIRST  LESSONS  is  illustrated  with  up- 
wards of  sixty  original  engravings  executed  in  the 
finest  style  of  art,  and  forms  one  of  the  most 
attractive  books  for  the  young  ever  published. 

FELTER'S  PRIMARY  is  also  elegantly  illustrated 
with  a  number  of  suggestive  engravings,  illustrating 
the  Fundamental  Rules  and  Denominate  Tables. 

N.  B. — For  the  use  of  Private  Schools  the  IN- 
TERMEDIATE and  GRAMMAR-SCHOOL  books  are  bound 
in  one  volume,  and  called  the  "  PRACTICAL/' 

*  This  book  is  intended  expressly  for  High  Schools  and  Universities, 
•where  particular  attention  is  given  to  the  theory  of  numbers  and  ad- 
vanced commercial  instruction. 


INTRODUCTION, 


SUGGESTIONS  TO  TEACHERS. 

WE  hope  a  few  suggestions  on  the  subject  of  teaching  arithmetic 
will  not  be  taken  amiss  by  those  .teachers  who  may  desire  to  use  this 
little  book.  There  is  danger. in  teaching  any  of  the  elementary 
branches,  of  falling  into  a  habit  of  monotony  which  soon  robs  both 
teacher  and  pupil  of  nearly  all  the  interest  they  would  otherwise  feel 
in  these  studies.  Variety  in  the  exercises  and  in  the  methods  of  reci- 
tation are  indispensable  to  a  permanent  interest  in  any  study,  and 
especially  in  elementary  arithmetic.  We  propose,  therefore,  in  a 
manner  as  brief  and  concise  .as  possible,  to  present  a  few  exercises, 
and  give  a  few  methods  of  recitation,  not  as  the  best  or  the  only 
ones,  but  merely  as  suggestions  to  the  ingenious  teacher. 

In  Notation  we  may  have, 

EXERCISE  i.  Copy,  on  the  blackboard  after  the  class  have  previously 
copied  the  same  on  their  slates,  say,  Lesson  in ;  let  the  teacher 
point  to  an  exercise,  No.  5,  for  instance,  and  require  the  class  to  read 
in  concert,  speaking  promptly,  and  together,  thus:  Four,  nine,  eight.. 
&c.  Let  the  teacher  continue  this  exercise  until  all  can  read  the 
numbers  readily  and  promptly. 

Ex.  ii.  Let  the  teacher  require  each  member  of  the  class  to  read 
the  sam6  alone,  until  each  one  can  read  quickly  and  accurately. 

Ex.  in.  Let  the  teacher  erase  the  numbers  from  the  blackboard, 
and  then  require  each  member  of  the  class  to  read  the  same  from 
his  slate,  the  teacher  noting  whether  the  It  s<on  has  been  correctly 
copied. 

Ex  iv.  Let  the  teacher  after  examining  the  mechanical  execution 
of  the  work,  and  requiring  it  to  be  erased,  proceed  to  dictate  the 
game  lesson  to  the  class.  Let  the  class  then  be  numbered  by  twos, 
and  at  a  signal  require  them  to  exchange  slates.  Let  the  teacher 
then  read  aloud  the  same  lesion  from  the  book,  and  require  each 


riii 


INTRODUCTION. 


pupil  to  note  the  errors  by  drawing  a  line  under  each  number  not 
correctly  written.  The  errors  should  then  be  reported  and  the  slates 
returned  to  their  owners.  . 

ADDITION.* — Ex.  v.  Let  the  teacher  require  the  pupil  to  commit 
and  recite  both  forms  of  the  table,  after  which  let  him  be  thoroughly 
questioned  on  the  same.  In  this  and  in  other  exercises,  the  teaehol 
will  find  that  the  practice  of  allowing  the  class  to  question  an  indi- 
vidual scholar,  or  a  scholar  to  question  his  class,  will  exercise  a  great 
influence  in  promoting  an  interest  in  the  study.  This  may  not,  at 
first,  seem  practicable,  but  experience  has  proved  the  results  emi« 
nentiy  satisfactory. 

Ex.  vi.  (See  note  f  Lesson  2.)      •  •    •    . 

Ex.  vii.  Let  the  teacher  read  to  the  class  an  example,  say,  Ex.  1, 
Lesson  1,  and  then  require  some  pupil  to  repeat  the  same  from  mem- 
ory, and  give  the  appropriate  solution  WITHOUT  HESITATION. 

Ex.  vui.  Let  the  teacher  read  aii  example  for  each  member  of  the 
class,  without  waiting  for  a  solution,  and  then  require  the  solution  of 
each  example  in  the  order  in  which  it  was  read. 

Ex.  ix.  Let  the  teacher  require  the  class  to  sit  or  stand  in  a  cer- 
tain position,  and  then  dictate  numbers  to  be  added  by  them  men- 
tally and  silently,  thus :  the  teacher  says,  (the  class  being  in  an  ex- 
ercise of  fours,)  "Thr-ee,  two,  one,  two,  four,"  &c.,  to  thirty  or  forty. 
When  the  teacher  has  finished;  at  a  given  signal  all  the  class  should 
raise  their  hands.  Let  the  teacher  require  some  one  to  give  the  sum, 
and  all  who  agree  with  the  result  thus  given  to  take  down  their  hands. 
If  any  hands  remain  up,  let  the  teacher  call  upon  another,  &c.,  until 
all  are  down,  when  he  should  announce  the  correct  result.  Care  should 
be  taken  that  this  exercise  be  not  so  difficult  as  to  prevent  any  from 
joining  in  it. 

Ex.  x,  After  the  class  have  properly  prepared  their  written  exer 
cises,  let  the  teacher  call  for  the  sum  of  a  certain  example  by  nunj- 
ter,  and  require  some  member  of  the  class  to  read  it.  All  who  agree 
\vith  the  answer  thus  read,  should  raise  the  hand ;  if  not  correct,  let 
another  be  called  upon,  &c.  Finally,  let  the  teacher  announce  the 


^Nearly   ail   the   follo-.ving  exercises    are  equally    applicable   to    the    rules 
Subtraction,  Multiplication  iinJ  Division 


txxiiOD  LOTION.  ix 

correct  result,  and  require  each  member  of  the  class  to  note  his  errors 
oy  drawing  a  line  under  each  incorrect  answer. 

Ex.  xi.  As  often  as  practicable,  let  the  teacher  dictate  numbers, 
to  be  added  on  the  siute  as  a  class  exercise.  Rapidity  and  accuracy 
should  be  the  results  sought  for. 

SUBTRACTION. — The  teacher  should  give  particular  attention  to  the 
explanation  of  the  method  of  subtraction.  The  old  method  of  "  bor- 
rowing ten  and  carrying  to  the  next  lower  left  hand  figure  to  pay  it7n 
should  become,  as  it  now  is  in  our  best  schools,  obsolete.  The  new 
method  can  be  found  fully  explained  in  the  First  Book  of  the  "Arith- 
metical Analysis." 

DIVISION. — It  is  very  important  that  the  two  forms  of  Division  be 
distinctly  explained  to  the  class  before  they  are  required  to  solve  the 
mental  examples  under  that  rule.  It  can  readily  be  made  plain^ 
thus :  Take  a  number  of  cents,  place  them  in  a  pile,  and  then  divide 
it  into  a  given  number  of  equal  parts.  This  is  separating  the 
Dividend  into  as  many  parts  as  there  are  units  in  the  Divisor,  and 
hence  it  may  be  called  Division  Proper/* 

Again,  place  the  cents  in  a  pile  as  before,  and  then  ask  how  many 
oranges  can  be  purchased  at  3  cents  each.  As  many  oranges  can  be 
purchased,  as  the  number  of  times  3  cents  can  be  subtracted  from 
the  number  of  cents  contained  in  the  pile;  and  the  8  cents  can  be 
subtracted  from  the  pile,  as  many  times  as  3  cents  are  contained  in 
the  number  of  cents  in  the  pile.  This  is  Division  by  subtracting  the 
Divisor  a  certain  number  of  times,  (indicated  by  the  Quotient,)  from 
the  Dividend,  and  hence  may  be  called  Division  by  Subtraction.* 

CLASSIFICATION. — Teachers,  and  especially  those  of  our  ungraded 
public  schools,  often  complain  that  the  time  for  the  recitation  of  each 
etudy  is  necessarily  too  Short.  While  we  admit  the  justice  of  tlu> 
complaint  we  think  the  difficulty,  to  some  extent,  may  be  obviated 
by  giving  more  attention  to  classification.  This  we  think  especially 
true  ia  regard  to  Arithmetic.  Generally,  there  is  more  time  WASTED 
in  Jiesitationt  than  is  USED  in  actual  recitation.  In  ten  minutes  of 


* These  terms  though  uot  philosophically  correct,  yet  perhaps  will  more 
distinctly  point  out  tae  aill^resce  to  a  child  than  tho;e  implicating  u  knowledge  o/ 
factors. 


i  INTRODUCTION. 

active,  prompt  recitation,  more  can  be  accomplished  than  in  thirty 
spent  in  hesitating  and  blundering.  The  teacher  who  attempts  to 
gain  time  by  crowding  into  one  class  scholars  of  different  grades  01 
progress  and  ability,  in  order  to  limit  the  number  of  recitations,  com- 
mits a  grave  error.  If  he  has  too  many  studies  in  the  school,  it  is 
better  to  drop  some  of  them,  for  Reading,  Writing  and  Arithmetic 
WELL  learned,  are  far  better  than  a  smattering  of  the  whole  range  of 
science.  When  dull,  slow,  and  young  pupils  are  placed  in  a  class 
with  those  who  are  quicker  and  older,  being  continually  surrounded 
by  a  maze  of  difficulties,  they  are  necessarily  soon  discouraged,  and 
consume  more  of  the  teacher's  time  in  explanation  than  the  whole 
class  should  consume  in  recitation.  The  quick  and  active,  from  not 
being  allowed  to  exercise  the  full  scope  of  their  powers,  soon  contract 
the  habit  of  lazy  carelessness.  In  schools  where  proper  classification 
is  neglected,  idleness,  carelessness 'and  inattention  must  necessarily 
exist.  ...'.';:..'... 

THOROUGHNESS.— The  importance  of  being  thorough  in  the  ele- 
ments of  Arithmetic  can  not  be  too  often  impressed  upon  the  teacher. 
He,  influenced  by  a  strong  desire  to  please  both  parent  and  pupil,  is 
subject  to  a  great  temptation  to  hurry  his  scholars  through  text-books 
faster  than  is  consistent  with  their  best  interests.  Parents  are,  gen- 
erally, far  more  practical  than  ttie  teacher,  and  although  they  may 
for  a  time  be  deceived  by  book  progress,  yet  their  keen  perceptions 
of  practical  results,  will  soon  discover  the  flimsy  cheat,  and  hold  the 
author  in  just  contempt.  •;"'.- 

In  order  to  secure  thoroughness,  give  short  lessons,  and  spend 
much  time  in  daily  review.  If  in  the  exercise  of  "fours,"  do  not  pro- 
ceed until  everything  that  precedes  is  as  familiar  as  the  alphabet. 
If  it  requires  one  month,  take  it,  if  one  year,  the  time  can  not  be  bet 
ter  spent.  Never  allow  a  pupil  who,  habitually,  misses  over  ten  per 
cent,  of  the  given  exercise  to  remain  in  the  class,  for  it  is  far  better 
for  a  scholar  to  be  at  the  head  of  a  low  class,  than  at  the  foot  of  a 
high  one.  Never  rob  your  scholars  of  the  credit  due  their  efforts  by 
asserting  continually  that  their  lessons  are  easy ;  rather  cultivate  their 
self-confidence  by  causing  them  to  feel  a  conscious  ability  10  do  even 
more  than  you  require  of  them. 


SECTION   I. 
NOTATION  AND  NUMERATION. 


LESSON    I. 

Written.  Printed.  Roman. 


One 


pump  ; 


^  1  ;  I. 


Two  bouses  ;   2/  2;  II. 


>/  3;  III. 


Four  men  ;      ^-  4;   IV. 
Five  trees  ;      £ f-  5;   V. 


Six  birds ; 


Written.  Printed.  Roma 

^/6:  VI. 


/SW-^w  windows  ;  /V  7;  VII. 
Eight  geese;       ^-8;  VIII. 


ine  sheep ; 

posts ; 


'/  9 ;  IX. 
10;  X. 


NOTATION    AND    NUMERATION. 

LESSON   II. 
EXERCISES  IN  NOTATION. 


Figures       Figures     N-_-. 
as  written,  as  printed.  * 

Figures        Figures      N 
as  \vritten.  as  printed.    * 

0            0 

naught. 

15       15 

fifteen. 

/            1 

one. 

1b     16 

sixteen. 

2       2 

two. 

//       17 

seventeen. 

3         3 

three. 

18    is 

eighteen. 

4         4 

four. 

iq     19 

nineteen. 

5       5 

five. 

20      20 

twenty. 

b      6 

six. 

21       21 

twenty-one, 

7         7 

seven. 

22       22 

twenty  -two. 

$        8 

eight. 

30      30 

thirty. 

<r    9 

nine. 

40     40 

forty. 

to     10 

ten. 

50        50 

fifty. 

//     11 

eleven. 

bo      eo 

sixty. 

12       12 

twelve. 

70       70 

seventy. 

13       13 

thirteen. 

80     so 

eighty. 

/4       14 

fourteen. 

CfO       90 

ninety. 

Figures  as  written  . 

Figures  as  printed. 

Names. 

100 

100 

one  hundred. 

200 

200 

two  hundred. 

300 

300 

three  hundred. 

101 

101 

one  hundred 

and  one. 

102 

102 

one  hundred 

and  two. 

103 

103 

one  hundred 

and  three. 

111 

111 

one  hundred 

and  eleven. 

112 

112 

one  hundred 

and  twelve. 

113 

113 

one  hundred 

and  thirteen. 

120 

120 

one  hundred 

and  twenty. 

NOTATION    AND    NUMERATION.  O 

LESSON  III. 

•Copy  and  read  the  following  numbers: 

(1)     (2)    (3)     (4)     (5)     (6)     (7)     (8)     (9)-(10)(ll)(12,  ;i3) 


47  87  8  37  43,  qq  8  4 
5oq8778qss  t  3  g 
bq-tqtq387qb43 

7  b  b  iq8qq5$774 
8073b38lbbS8t 


LESSON  IV. 
(1)    (2)     (3)    (4)    (5)    (6)    (7)    (3)    (9) 

to  30  40  50  40  40  40  80  40 

20  70  70  80  30  80  80  70  bO 

30  bO  80  70  qO  70  bO  30  qo 

40  80  bO  bO  qo  10  30  bO  80 

50  qo  20  qo  bO  00  qo  70  qo 

*  NOTE  FOR  THE  TEACHER.  —  The  teacher  should  require  these  exercises  to  be 
copied  neatly  upon  a  slate  or  paper,  and  read  as  a  class  exercise,  individually, 
or  by  the  class  in  concert.  Particular  attention  should  be  given  to  the  forma- 
tion of  the  ^  figures. 

N.  B.—  The  teacher  should  not  fail  to  spend  a  portion  of  each  recitation  in 
dictating  numbers  to  be  written  by  the  class  ;  for,  unless  this  is  done,  only  half 
of  Notation  will  be  learned  We  would  suggest  that  the  teacher  dictate  each 
lesson  given  in  the  book,  each  pupil  copying  the  same  on  the  slate  as  it  is  dic- 
tated. Let  each  pupil  then  exchange  slates  with  his  neighbor,  and  note  the 
errors  made  by  him,  by  drawing  a  line  under  each  number  not  correctly  written, 
while  the  teacher  again  reads  the  numbers  from  the  book,  thus  making  each 
pupil  a  critic  upon  his  neighbor's  work.  Continue  this  exercise  until  the  class 
can  write  as  accurately  as  they  read.  A  record  of  the  recitation  of  each  pupil 
should  be  kept  for  reference. 


4  NOTATION  AND  NUMERATION. 

bO  70  W  80  70  qo  qO  80  30 

70  bO  qo  80  50  70  70  bO  80 

80  00  bO  70  bO  bO  bO  70  70 
qO  30  30  bO  30  70  30  30  In 

LESSON  V. 
(1)    (2)   (3)   .(4)    (5)    (6)   (7)    (8)   (9)   (10) 

QQ  qq  55  qq  22  55  44  44  qq  44 

bb  77  $8  33  11  88  11  bb  bb  22 
44  88  77  77  88  44  77  22  44  88 

22  bb  88  //  bb  33  bb  33  55  55 

88  44  bb  55  22  55  44  77  88  77 

77  22  44  77  55  22  77  22  oo  55 

33  77  bb  55  22  88  22  bb  ft  00 

44  //  77  44  //  22  33  11  88  77 

LESSON  VI. 
(1)   (2)   (S)   (4)    (5)    (C)    (7)    (8)    (9)    (10) 

2t  41  qi  bl  31  72  32  b2  72  b2 
31  81  b1  qi  81  82  42  32  32  52 

71  71  31  81  qi  q2  72  52  22  32 

81  bf  41  31  bt  32  b2  b2  12  72 
b1  q/  81  41  71  72  32  72  q2  b2 
81  1151  81  51  b2  82  32  52  72 
41  41  qt  bt  5f  22  22  52  q2  52 
qi  51  71  51  3f  52  22  52  22  12 


NOTATION    AND    NUMERATION.  5 

LKSSON  VII. 

(1)         (2)         (3)  (4)          (5)          (C)  (-.)          (8)          (9) 

33  33  b3  14  b4  34  b5  25  q5 

23  53  43  J4  34  *4  35  b5  75 

53  73  23  b4  q4  54  75  55  35 

b3  53  q3  54  24  34  55  25  q5 

53  73  q3  14  24  54  15  25  b5 

q3  43  S3  54  24  74  b5  25  75 

73  23  43  q4  74  54  75  b5  25 

q3  q3  13  54  04  b4  55  15  b5 

LESSON  VIII. 

(1)   (2)   (3)   (4)  (5)   (6)   (1)   (8)  (9)  (10).  (11)  (12) 

66  76  36  11  37  57  18  68  78  69  49  79 

86  46  86  17  67  17  28  38  88  99  69  69 

96  86  76  27  57  87  38  58  08  19  89  89 

46  96  96  87  67  67  68  78  98  09  39  99 

86  76  66  37  97  97  98  38  78  29  79  29 

46  86  86  47  87  87  88  68  68  39  69  39 

96  46  06  67  37  37  78  88  38  69  39  79 

86  76  76  97  67  47  98  78  78  89  89  69 

LESSON  IX. 

(1)   (2)   (3)   (4)  (5)   (6)   (7)   (8)  (9)  (10)  (11)  (12) 

46  68  80  56  68  46  41  41  68  41  41  37 

89  37  60  11  74  83  86  89  93  83  89  86 

78  89  37  10  83  98  91  67  97  67  67  97 

37  34  34  01  89  30  87  83  83  83  83  83 
66  76  04  11  67  67  83  91  97  97  84  89 
41  46  66  13  03  83  68  73  86  86  89  67 

38  89  99  22  09  97  78  91  67  67  76  60 
70  70  78  33  70  81  32  37  83  83  86  30 


6  NOTATION    AND    NUMERATION. 

LESSON  X. 

(1)        (2)        (3)        (1)       (5)        (6)        (7)  (8)        (9)        (10) 

100  800  900  GOO  900  888  888  .999  777  999 

200  600  400  800  600  666  333  888  888  888 

300  900  600  300  300  444  777  333  333  666 

400  300  900  700  700  333  333  111  777  777 

500  600  400  600  800  999  888  222  666  333 

600  800  300  300  900  666  666  333  888  444 

LESSON  XI. 

(1)   (2)   (3)   (4)   (5)   (0)   (7)  (8)   (9)   (10) 

146  156  157  187  178  273  246  286  278  278 

186  186  168  107  108  286  289  273  286  283 

174  137  193  100  101  2.07  278  243  '237  296 

145  182  107  186  100  201  -  209  262  241  271 

183  193  109  106  198  271  290  283  262  240 

197  178  108  108  000  268  270  291  268  240 

LESSON  XII. 

(1)   (2)   (3)   (4)   (5)   (6)   (7)  (8)   (9)   (10) 

378  396  407  507  637  707  880  960  437  110 

396  378  409  500  649  709  860  940  609  101 

347  307  403  569  687  700  893  980  708  001 

378  311  408  511  683  711  808  908  808  301 

386  341  400  522  621  701  880  960  607  103 

307  369  406  589  637  710  870  906  706  031 

LESSON  XIII. 

(1)           (2)           (3)            (4)              (5)  (6)              (7) 

1,000    4,000    4,000    46,000     83,684  33,870     66,907 

2,000    8,000    8,000    86,000     83,789  44,968     77,003 

6,000     6,000     6,000     97,000     83,986  55,708     88,806 

8,000    9,000    9,000    37,000     83,689  88,070     33,403 

9,000    7,000    3,000     40,000     83,417  66,407     66,907 

3,000    3,000    7,000    80,000     83,404  88,006    44,603 


NOTATION    AND    NUMERATION. 


LESSON   XIV.* 


(1) 

91,868 
91,674 
91,410 
91,800 
91,410 
91,001 
91,625 

(2) 
65,870 
65,001 
65,680 
65,012 
65,101 
65,001 
65,200 

(3) 
87,000 
87,408 

87,007 
87,008 
87,680 
87,708 
87,905 

(4) 

41,734 

68,783 
91,860 
41,307 
40,037 
86,013 
45,702 

41 
91 
38 
41 
89 
41 
27 

(5) 
,862 
,878 
,786 
,837 
,186 
,837 
,529 

(6) 
41,864 

89,608 
91,837 
60,382 
46,867 
89,371 
95,296 

m 

41,890 
60,004 
90,008 
30,100 
70,864 
01,010 
20,002 

LESSON   XV. 


(1) 

467,918 
467,001 
467,3r>8 
467,001 
467,000 
467,781 
467,525 

(2) 

460,891 
460,013 
460,108 

460,03:) 
460,660 
460,141 
463,262 

(3) 
200,040 
200,110 
200,301 
900,041 
900,008 
900,903 
500,244 

(4) 
307,064 
309,083 
631,837 
001,301 
607,013 
901,803 
209,502 

(5) 

401,864 

908,864 
301,837 

003,907 
900,869 
701,803 
450,002 

(6) 
301,413 
401,108 

600,307 
900,609 
801,300 
608,400 
572,909 

LESSON   XVI. 


(1) 

(2) 

(*) 

(4) 

1,000,000 

9,444,444 

5,600,800 

8,786,413 

6,000,000 

8,333,333 

3,700,900 

'   9,187,687 

8,000,000 

6,888,883 

9,000,600 

8,913,418  j 

9,000,000 

4,777,777 

3,007,007 

6,701,384 

4,000,000 

3,666,666 

8,004,004 

8,870,018 

8,000,000 

9,111,111 

2,001,001 

3,896,041 

7,000,000 

2,555,555 

1,060,200 

5,473,256 

NOTE  FOR  THE  TEACHER.— The  Author  does  not  intend  to  make  a  hook  *i 
,take  the  place  of  the  living  teacher,  consequently  he  does  not  wish  to  burden 
its  pages  with  explanations  and  remark*  about  subjects  with  which  the  teacher 
!•»  perfectly  familiar.  His  object,  as  before  stated,  is  to  aid  the  teacher  in  giving 
tlie  pupil  SOMETHING  TO  DO  The  teacher  can  explain  to  the  pupil  the  how  and 
the  why.  much  better  than  the  author 


SECTION  II. 
LESSON  II. 

1.  There  are  4  bushels  of  salt  in  1  bag,  and  2  in 
anotber ;    bow  many  bushels  in  both  ? 

FORMULA. — If  there  are  4  bushels  of  salt  in  one  bag,  and  2  bushels 
in  another,  there  is  in  both  the  sum  of  4  bushels  and  2  bushels,  which 
is  6  bushels ;  therefore  in  both  bags  there  are  6  bushels. 

2.  Charles  had  2  marbles,  his  brother  gave  him   one 
more ;    how  many  had  he  then  ? 

3.  Susan  had  3  pins  in  her  cushion,  she  found  1  more; 
how  many  pins  had  she  then  ? 


ADDITION, 


LESSON    II. 

TABLE.* 

1 

and 

0 

are 

1. 

2 

and 

0 

are 

2. 

1 

and 

1 

are 

2. 

1 

and 

2 

are 

3. 

2 

and 

1 

are 

3. 

2 

and 

2 

are 

4- 

3 

and 

1 

are 

4. 

3 

and 

2 

are 

5. 

4 

and 

1 

are 

5. 

4 

and 

2 

are 

6. 

5 

and 

1 

aro 

6. 

5 

and 

2 

are 

7. 

6 

and 

1 

are 

7. 

6 

and 

2 

are 

8. 

7 

and 

1 

are 

8. 

7 

and 

2 

are 

9. 

8 

and 

1 

are 

9. 

8 

and 

2 

are 

10. 

9 

and 

1 

are 

10. 

9 

and 

2 

ere 

11. 

ID 

and 

1 

are 

11. 

10 

and 

2 

are 

12. 

BLACKBOARD    EXERCISES. 


(3) 


IM 

4 

4 

fi 

t5 

6 

8 

9 

1 

J2 

2 

1 

2 

2 

2 

2 

2 

2 

2 

2 

— 

— 

— 

— 

— 

2 

2 

2 

2 

2 

1 

(2) 

2 

2 

*2 

0 

2 

3 

7 

4 

2 

2 

1 

2 

2 

2 

2 

2 

2 

2 

1 

— 

— 

— 

— 

— 

2  ' 

2 

2 

2 

1 

2 

NOTES  FOR  TEACHERS. — *  The  pupil  should  be  required  to  commit  both  forms 
of  the  Addition  tables  ;  and  beside  this,  the  teacher  should  thoroughly  question 
him  upon  them,  until  he  becomes  accurate  and  prompt  in  his  answers. 

t  The  teacher  should  copy  these  exercises  upon  the  blackboard,  and,  pointing 
)o  each  of  the  columns  successively.,  require  a  pupil,  or  the  class  in  concert,  to 
name  tiie  sum  of  each  column  instantaneously:  thus  (pointing  to  the  left-hand 
column)  the  pupil  should  say,  "Seven;'-  not,  "Two  and  five  are  seven:" 
pointing  to  the  next  column,  the  pupil  should  at  once  say,  "Eight;"  not, 
*  Two  and  six  are  eight  " 

3.  These  exercises  in  adding  columns  at  sight,  should  be  practiced,  in  the  fol- 
lowing manner  :  Copy  the  exercise  on  the  blackboard  ;  let  a  pupil,  or  the  class 
In  concert,  commence  at  the  bottom  and  add,  repeating  only  the  result  of  each 
addition  ;  thus,  {Exercise  3rd,)  2,  4,  6,  8,  10,  12,  &c.,  to  fifty  or  more,  as  the 
teacher  mi/  judge;  bost  Let  the  tables  and  exercises  be  thoroughly  learnedf 
for  ••  \\\i  .t  i.;  woi'tii  doing  at  all,  i«  wo*rh  doing  WELL." 


10  ADDITION. 

LESSON  III. 
MENTAL  EXERCISES. 

1.  John  has  5  apples,  and  his  father  gives  him  2  more; 
r        how  many  has  he  then  ? 

SOLUTION. — If  John  has  5  apples,  and  his  father  gives  him  2 
more,  he  then  has  the  sum  of  5  apples  and  2  apples,  which  is  7 
apples. 

Therefore,  if  John  has  5  apples,  and  his  father  gives  him  2 
more,  he  then  has  7  apples. 

2.  James  has  six  apples,  and  buys  one  more;  how 
many  apples  has  he  then  ? 

3.  If  I  buy  2  quills  for  two  cents,  and  4  quills  for  4 
cents,  how  many  quills  have  I  ? 

4.  Henry  has  two  tops,  and  buys  4  others ;  how  many 
has  he  then  ? 

5.  If  you  buy  2    peaches  for    two    cents,  and    nine 
peaches  for  9  cents,  how  many  do  you  buy  in  all? 

6.  Susan  has  2  cherries  in  her  hand,  and  has  just  given 
*  away  7 ;  how  many  had  she  at  first  ? 

7.  Laura  had  6  apples,  and  her  mother  gave  her  2 
.  more ;  how  many  had  she  then  ? 

8.  George  bought  5  marbles,  and  his  brother  gave  him 
2  more  ;  how  many  had  he  then  ? 

9.  If  I  buy  2  tops  for  eight  cents,  and  6  tops  for  12 
cents,  how  many  tops  do  I  buy  in  all? 

10.  If  I  buy  2  tops  for  eight  cents,  and  4  tops  for  2 
cents,  what  do  my  tops  cost  me  ? 

11.  If  I  buy  a  slate  for  10  cents,  and  a  pencil  for  2 
cents,  what  do  both  cost? 

12.  John  sold  a  knife  for  9  cents,  and  a  pencil  for  2 
cents;  how  much  did  he  receive  for  both? 


ADDITION.  11 

LESSON    IV. 
WRITTEN  EXERCISES, 

In  which  the  sum  of  each  column  does  not  exceed  nine. 

(1)         (2)         (8)          (4)          (5)          (6)          (7)  (8)  (9) 

201      320      102      210      210      012      102  102  200 

012      212      210      102      102      200      222  201  102 

201      102      102      222      201      002      100  202  201 

210      201      201      102      200      102      210  221  222 


(10)        (11)  (12)  (13)  (14)  (15)  (16)  (17) 

1012  2012  2012  2012  2102  2010  220i  2121 

0121  0122  2012  2001  2011  0121  2012  0121 

2012  0101  2120  0211  0121  2012  1021  2012 

1012  -  2012  1012  0222  2010  1012  1021  2012 


LESSON  V. 

(18)     (19)     (20)     (21)     (22)  (23) 

10212  21212  21210  21211  212112  21211 

21021  10212  20121  21221  212112  21211 

21102  22121  21021  10221  210211  21221 

20121  21120  10222  10212  102122  01211 


(24)  (25)  (2G)     (27)     (28)  (29) 

21212  21021  20121  21012  21221  21211 

12110  20122  92110  20121  21012  22122 

02102  21021  21012  10122  22011  20121 

21022  20122  22101  20121  21012  10121 


(30)  (31)  (32)  (33)  (34)  (35) 

10121  21021  20121  21210  21021  21012 

21012  20112  21122  21012  20112  20112 

210  22102  02122  21101  10221  01221 

1012  10121  21012  10210  20121  20121 


12 


ADDITION. 


LESSON   VI. 


1  and  3  are  4. 
2  and  3  are  5. 
3  aud  3  are  6. 

TABLE. 

4  and  3  are  7, 
5  and  3  arc  8. 
6  and  3  are  9. 

Table  Exercise. 

7  and  3  are  10. 
8  and  3  are  H. 
9  and  3  are  12. 

10  +  3  =  ?  11  4-  3=:?  12  +  3  =  ?  13  +  3  = 

20  +  3  =  ?  21  +  3  =  ?  22 •  +  3  =  ?  23  +  3  =  ?  24  +  3  =  ?  etc. 
30  +  3  =  ?  31  +  3  =  ?  32  +  3  =  ?  33  +  3  =  ?  34  +  4  =  ?  etc. 
etc.  etc.  etc.  etc.  etc. 

NOTE.— The  above  and  following  Table  Exercises  should  be  extended 
and  completed  on  the  slate  or  blackboard,  and  the  pupils  drilled  upon 
them  until  every  combination  is  thoroughly  learned. 


0 
3 


3 
3 


7 
3 


BLACKBOARD   EXERCISES 

(3) 

(4) 

(5) 

(?) 

(1) 

<§ 

G 

B 

4 

0 

9 

2 

8 

3 

3 

3 

1 

3 

3 

3 

3 

3 

3 

3 

— 

— 

— 

3 

3 

3 

2 

3 

3 

3 

2 

(2) 

3 

3 

3 

1 

4 

6 

5 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

2 

— 

— 

— 

3 

1 

2 

1 

NOTE. — These  exercises  are  to  be  recited  in  the  same  way  as  the  similar  exer- 
cises preceding. 

LESSON    VII. 
MENTAL  EXERCISES. 

1.  Charles  has  3  nuts  in  one  hand  and  3  in  the  other; 
how  many  has  he  in  both? 

SOLUTION. — The  same  as  in  Lesson  II. 

2.  Oscar  has  5  pencils,  and  Joshua  has  3  ;  how  many 
have  both  ? 

3.  William  has  three  rabbits,  and  Henry  has  9  ;  how 
many  have  both  ? 


ADDITION.  13 

4.  Ella  has  4  birds  in  one  cage,  and  3  in  another:  how 
many  has  she  in  both  ? 

5.  Myra  had  8  pins  in  her  cushion,  and  then  put  in  3 
more ;  how  many  had  she  then  ? 

6.  Carrie  had  3  needles,  and  then  bought  eight ;  how 
many  had  she  then  ? 

7.  John  buys  4  tops  for  12   cents,  and  3  tops  for  9 
cents ;  how  many  tops  has  he  in  all  ? 

8.  George  buys  3  pears  for  four  cents,  and  two  pears 
for  3  cents ;  how  much  do  his  pears  cost  him  ? 

9.  Julius  bought  10  pears  for  10  cents,  and  three  pears 
for  three  cents;  how  much  did  they  cost  him? 

10.  Charles  has  no  rabbits,  and  Henry  has  three;  how 
many  have  both  ? 

11.  Alfred  caught  3  birds,  and  Jason  caught  one ;  how 
many  did  they  both  catch? 

12.  James  had  2  marbles,  and  afterward  won  9  from 
Charles  ;  how  many  had  he  then  ? 

13.  If  an  orange  costs  3  cents,  and  4  oranges  cost  7 
cents,  how  much  do  all  cost? 

14.  Gertrude  had  3  cents  given  her  by  her  uncle,  then 
her  mother  gave  her  9  more ;  how  many  cents  nad  she 
in  all  ? 

LESSON  VIII. 
WRITTEX  EXERCISES. 


(36) 

(37) 

(38) 

(39) 

(4ty 

(41) 

(42) 

3101 

2031 

3012 

31012 

31213 

2123 

3121 

2103 

2103 

3331 

32103 

12132 

3211 

2103 

2101 

3011 

1032 

13312 

21312 

2312 

1331 

0133 

3011 

0301 

23331 

31011 

1031 

0112 

14 


ADDITION. 


(43)  (44)  (45)  (46)  (47)  48)  (49)  (50) 

3132  3102  3103  3102  3102  3121  2132  3121 

2132  1031  0132  3012  0312  0130  1201  0301 

0301  3012  3213  0131  3101  2132  3103  1333 

3012  3111  3011  2132  2132  H13  2301  2233 


LESSON  IX. 

*Exercises  in  which  the  sum  of  each  column 
ten,  but  is  less  than  twenty. 
(51)          (52)          (53)          (54)  (55) 

3121*  3132  1323  3103  31213 

3233  2133  2323  3213  23132 

3233  3032  3223  2133  21332 

2332  3321  3332  3321  33213 

3123  3333  2332  2332  23323 

3321  2332  3212  0323  32133 


equals  or  exceeds 


(56) 

31232 
32133 
32332 
32223 
23322 
12233 


(57) 

3123 

2323 

3233 

2132 

3212 

3332 


(58)  (59) 

31333  21321 

23213  01332 

31220  32132 

33303  32013 

10332  32103 

12321  23321 


(60)     (61) 

32212  23213 

31232  23223 

"21332  32213 

21321  33223 

33233  13322 

13321  32332 


(62)     (63) 

32213  32132 

32123  02321 

32233  31223 

32213  20301 

32132  21303 

21331  33233 


(64)  (65)  (66)  (67)  (68)     (69)  (70) 

2133  2132  3213  32212  23121  23321  24323 

3103  3233  2232  33132  32221  30232  22322 

2332  3213  2232  22322  33233  23213  32132 

2332  2303  2232  33232  23213  32332  32232 

3212  1332  3213  10232  20322  23323  23312 


*  NOTE  FOR  THE  TEACHER.— Before  performing  these  exercises,  the  teacher 
ihould  take  occasion  to  explain  to  the  class  the  method  of  carrjing.  The 
teacher  can  explain  it  in  his  own  way  much  better  than  the  author  could,  should 
he  attempt  it. 


ADDITION. 


15 


1  and  4  are  5. 

2  and  4  are  6. 

3  and  4  are  7. 


7  and  4  are  H. 

8  and  4  are  12. 

9  and  4  are  13. 


LESSON    X. 

TABLE. 

4  and  4  are     8. 

5  and  4  are     9. 

6  and  4  are  10. 

Table  Exercise. 

.  _9  12  +  4=?  13  +  4  —  ?  14  +  4  =  ?  e'c. 

-  =  ?  21+4  =  ?  22  +  4=?  23  +  4  =  ?  24  +  4  =  ?  eic. 

30  +  4  =  ?  31+4  =  ?  32  +  4  =  ?  33  +  4  =  ?  34  +  4  =  ?  etc. 

40  +  4  =  ?  41+4  =  ?  42  +  4  =  ?  43  +  4  =  ?  44  +  4  =  ?  etc. 

50  +  4  =  ?  51+4  =  ?  52  +  4  =  ?  53  +  4  =  ?  54  +  4  =  ?  etc. 
etc.       etc.       etc.       etc. 


etc. 


BLACKBOARD     EXERCISES. 


(3)      (4)      (5)      (6)      (7) 


0) 


1 

9 

2 

0 

8 

4 

4 

4 

4 

4 

(2) 

3 

7 

4 

6 

5 

4 

4 

4 

4 

4 

4 

4 

4 

4 

1 

4 

4 

4 

4 

4 

4 

4 

4 

4 

2 

4 

4 

4 

4 

3 

4 

4 

4 

4 

2 

4 

4 

4 

4 

1 

4 

4 

4 

4 

4 

4 

1 

2 

3 

1 

NOTE. — See  similar  preceding  exercises  and  the  method  of  recitation. 

LESSON  XI. 
MENTAL  EXERCISES. 

1.  There  are  4  boys  in  the  first  class,  and  4  in  the 
second  class  ;  how  many  in  both  classes  ? 

XOTE. — The  solution  is  the  same  as  in  the  preceding  exercises. 

2.  Samuel  drives  4  cows  to  pasture,  and  Lewis  drives 
rive  ;  how  many  do  both  drive  ? 

3.  A  dairyman  made  4  cheeses  in  one  week,  and  6  in 
-mother;  how  many  cheeses  did  he  make  in  both  weeks? 


16  ADDITION. 

4.  A  grocer  sold  four  pounds  of  rice  to  one  man,  and 
9  pounds  to  another ;  how  many  did  he  sell  to  both  ? 

5.  A  merchant  sold  7  yards  of  calico  to  one  customer, 
and  4  to  another ;  how  many  did  he  sell  to  both  ? 

6.  Thomas  had  4  sheep  in  one  pasture,  and  10  in  an- 
other ;  how  many  had  he  in  both  ? 

7.  Samuel  bought  2  sheep  for  9  dollars,  and  2  lambs 
for  4  dollars ;  how^much  did  they  all  cost  him  ? 

8.  If  4  scholars  sit  on  one  bench  and  1 1  on  another, 
how  many  sit  on  both  ? 

9.  There  are  10  scholars  in  the  school-house,  and  4 
are  having  a  recess ;  how  many  scholars  in  the  school  ? 

10.  There  are  4  broken  panes  of  glass  in  one  window, 
and  none  in  another ;  how  many  in  both  ? 

11.  If  it  is  4  miles  from  Newark  to  Belleville,  and  8 
from  Belleville  to  Patterson,  how  far  is  it  from  Newark 
to  Patterson? 

12.  If  there  are  9  dozen  sheets  of  paper  in  one  pile, 
and  4  dozen  in  another,  how  many  dozen  in  both  piles  ? 

13.  One  string  is  4  inches  long,  another  is  10  inches; 
how  many  inches  long  are  both  ? 

LESSON  XII. 
WRITTEN  EXERCISES. 

(71)    (72)    (73)    (74)    (75)  (76)  (77)  (78) 

3412  4123  4123  1230  2132  4132  2134  2413 

4324  4223  4032  4023  3142  0413  2443  4142 

2134  1443  3423  4243  3041  4413  2413  JD413 

2041  0343  2432  0243  2414  2142  1411  3042 

3412  2402  4243  2423  4421  4414  3424  4101 

2132  2401  3243  4331  3414  3041  4341  3401 


ADDITION. 


17 


(79) 

(80) 

(SI) 

(82) 

(83) 

(84) 

34124 

41234 

24134 

41234 

41341 

21314 

31413 

32134 

24413 

44341 

24143 

44143 

24130 

24341 

34123 

24132 

34124 

21321 

24133 

43214 

41244 

41421 

34143 

40143 

40241 

43441 

32412 

34134 

21414 

21434 

30213 

14234 

22141 

21414 

34140 

24143 

LESSON  XIII. 

Exercises  in  which  the  columns 

may,  or  may  not,  exceed  nine* 

(85) 

(86) 

(87) 

(88) 

(89) 

(90) 

41213 

41321 

41231 

41234 

41341 

24134 

40121 

41321 

11041 

43403 

40234 

32413 

30124 

40134 

41241 

40343 

34021 

21414 

13214 

40132 

32140 

30414 

34142 

32413 

12413 

40314 

44132 

34243 

43314 

41341 

(91) 

(92) 

(93) 

(94) 

(95) 

(96) 

34124 

4041 

41413 

41213 

41213 

32142 

41324 

3042 

21414 

12142 

40134 

30412 

14041 

4014 

34014 

40132 

41341 

40414 

30424 

3014 

40032 

40141 

04112 

30414 

40341 

3414 

40332 

20103 

30414 

23301 

LESSON 

XIV. 

• 

(97) 

(98) 

(99) 

(100) 

(101) 

(102) 

413412 

41321 

341412 

31401 

1 

41341 

321401 

43210 

14101 

2141 

41 

1412 

521403 

40142 

3041 

301 

371 

3 

413403 

02132 

14012 

2 

4142 

42 

240132 

41304 

44014 

42 

141 

1 

410321 

21401 

21011 

4132 

2 

9123 

18 


ADDITION. 


1  and  5  are  6. 

2  and  5  are  7. 

3  and  5  are  8. 


LESSON  XV. 


4  and  5  are     9. 

5  and  5  are  1Q. 

6  and  5  are  H. 


7  and  5  are  12. 

8  and  5  are  13. 

9  ai:d  5  are  14. 


Table  Exercise. 

104-5=?  11  +  5  =  ?  12  +  6=?  13  +  5  =  ?  14  +  6=?  etc. 

20  +  5=?  21  +  5  =  ?  22  +  5  =  ?  23  +  5  =  ?  24  +  5  =  ?  etc. 

30  +  5=?  31  +  5  =  ?  32  +  5  =  ?  33  +  5  =  ?  34  +  5  =  ?  etc. 

40  4-6  =  ?  41+5=?  42  +  5=?  43  -h  5  =  ?  44  +  5  =  ?  etc. 

50  +  5  =  ?  61  +  5  =  ?  52  +  5=?  53  +  5  =  ?  54  +  5=?  etc. 

elc~               etc.  etc.                etc.               etc. 


BLACKBOARD   EXERCISES. 


9 
5 


(1) 
0 

5 


(3)    (4)   (5)    (6)    (7)  '(8l 


5 

0 

5 

5 

5 

4 

5 

5 

5 

5 

,5 

5 

5 

5 

5 

5 

5 

i 

5 

5 

5 

5 

5 

2 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

1 

5 

5 

5 

5 

5 

2 

5 

1 

2 

3 

4 

3 

NOTE. — For  method  of  recitation,  see  similar  preceding  exercises 

LESSON  XVI- 
MENTAL  EXERCISES. 

1.  Susan  paid  five  cents  for  thread,  and  5  cents  foi 
needles ;  how  many  cents  did  she  pay  for  both  ? 

2.  Julia  has  six  little  books,  and  Jane  has  five ;  how 
,riany  have  both? 

3.  Ella  had  ten  cents,  and  her  mother  gave  her  five 
«nore;  how  many  had  she  in  all? 


ADDITION.  19 

4.  Henry  has  five  rabbits  in  one  cage,  and  7  in  an- 
other ;   how  many  rabbits  has  he  in  all  ? 

5.  A  traveler  inquiring  the  distance  to  a  hotel,  is  told 
that  it  is  eight  miles  to  the  first  house,  and  live  miles  from 
the  house  to  the  hotel ;  how  far  is  he  from  the  hotel  ? 

6.  John  went  fishing:  the  first  day  he  caught  8  perch, 
the  next  day  he  caught  5  trout ;   how  many  fish  did  he 
catch  during  both  days  ? 

7.  In  the  battle  of  Waterloo,  a  party  of  soldiers  cap 
tared  5  cavalry-men  at  one  time,  and,  shortly  after,  nine 
more ;  how  many  did  they  capture  in  all  ? 

8.  During  a  battle,  a  squad  of  soldiers  was  ordered  to 
fire  upon  the  enemy ;   9  discharged  their  pieces,  but  the 
remaining  5  disobeyed  the  order  :  how  many  men  wero 
there  in  the  squad  ? 

9.  If  a  wheel  turns  round  5  times  in  one  minute,  and 
3  times  the  next  minute,  how  many  times  does  it  turn 
round  in  the  two  minutes  ? 

10.  If  the  gold  coin  called  a  half-eagle  is  worth  5  dol- 
lars, and  the  eagle  is  worth  ten  dollars,  what  are  both 
worth  ? 

11.  If  I  shoot  5  pigeons  on  one  day,  and  10  the  next, 
how  many  do  I  shoot  on  both  days? 

12.  If  I  walk  11  miles  to-day,  and  5  miles  to-morrow, 
how  many  miles  do  I  walk  on  both  days? 

13..  If  you  carry  12  eggs  in  one  basket,  and  5  in  an- 
.ther,  how  many  do  you  carry  in  both? 

14.  A  California  gold-digger  obtained  9  oun?^s  of  gold 
from  one  hole,  and  five  from  another ;  how  many  did  he 
obtain  from  both  ? 


ADDITION. 


15.  A  little  boy  earned  5  cents  at  one  time,  and  13 
cents  at  another ;  how  many  did  he  earn  in  all  ? 


LESSON  XYII. 
WRITTEN  EXERCISES. 
*  Exercises  in  which  the  columns  may  or  may 
(103)        (104)         (105)       (106)       (107) 

4134  41304  3214  4132  3524 

4015  50152  4021  4132  5104 

3052  55013  4541  1443  3052 

4501  25214  4504  0545  4151 

2152  35241  0404  4052  3521 

1534  32141  3041  3052  4134 


(110) 

3214 
5105 
3042 
4132 
4014 
3214 

(ill) 
3412 
4152 
5214 
3241 
4045 
2041 

(112) 

31241 
45123 
40132 
40134 
44132 
40412 

(113) 

4134 
2414 
3424 
3541 
2413 
2414 

not  exceed  twenty, 

(108)  (109J) 

41324  3120 

14132  4152 

40413  5204 

24104  3052 

34114  4414 

04051  3240 


(114)  (115)  (116) 

3512  52134  4132 

3452  25152  4015 

4035  15354  5041 

4324  34345  4541 

4053  53050  3045 

5035  44014  3524 


(117)  (118) 

4512  4103 

3040  3042 

2453  4013 

2050  2413 

4305  0404 


LESSON  XVIII. 

(119)  (120)  (121) 

4132  4132  4132 

2412  4132  4213 

4521  4104  2441 

4525  2043  5253 

4525  2412  3525 


(122)  (123) 

4132  3524 

5245  3513 

3524  2413 

3514  2414 

4032  3243 


*  NOTE  FOR  THE  TEACHER.— The  teacher  should  take  occasion  to  explain  to  th« 
fupil  the  method  of  carrying  when  the  columns  exceed  nineteen. 


ADDITION. 


21 


1  and  6  are  7. 

2  and  6  are  8. 

3  and  6  are  9. 


10  +  6  =  ?  ll-f-6  = 
20  +  6=?  21  -f  6  = 
30-1-6  =  ?  31+6  = 
40  +  6  =  ?  41  +  6  = 
50  +  6  =  ?  51  +  6  = 
etc.  etc. 


LESSON   XIX. 
TABLE. 

4  and  6  are  10.     7  and  6  are  13. 

5  and  6  are  H.     8  and  6  are  14. 

6  and  6  are  12.     9  and  6  are  15. 

Talk  Exercise. 

?  12  +  6  =  ?  13  +  6=?  14  +  6=?  etc. 
?  22  +  6  =  ?  23  +  6  =  ?  24  +  6  =  ?  etc. 
?  32  +  6  =  ?  83  +  6  =  ?  34  +  6  =  ?  etc. 
?  42  +  6  =  ?  43  +  6  =  ?  44  +  6  =  ?  etc. 
?  52  +  6=?  53  +  6  =  ?  54  +  6  =  ?  etc. 
etc.  etc.  etc. 


8 
6 


(l) 

5  2 

6  6 


(2) 

6 
6 


BLACKBOARD  EXERCISES. 

(3)  (4)  (5)  (6)  (7)  (8)  (9) 

«3     6     O     O     G     CJ     G 

4   3    66666GG 

6   6    6666665 

66-66664 

6  6  G  6  6  6  3 

6  6  G  6  G  G  1 

0   7    6666QG4 

6   6    6123453 


NOTE. — See  similar  preceding  exercises. 

LESSON   XX. 
MENTAL  EXERCISES. 

1.  Julius  has  six  melons,  and  his  brother  has  six ;  how 
many  have  both  ? 

2.  Charlotte  has  9  roses  on  one  bush,  and  6  on  an- 
other ;  how  many  roses  has  she  in  all  ? 

3.  Mary  ate  3  peaches  before  dinner,  and  six  after 
dinner ;  how  many  did  she  eat  in  all  ? 


22  ADDITION. 

4.  If  I  buy  6  books  for   12  cents,  and  2  books  for* 6 
cents,  how  much  will  they  all  cost? 

5.  Joseph  bought  15   marbles  for  9  cents,  and  8  mar- 
bles for  6  cents ;  how  much  did  his  marbles  cost  him  ? 

6.  In  a  certain  orchard  there  are  six  pear-trees  and  8 
apple-trees ;  how  many  trees  in  the  orchard  ? 

7.  A  sportsman  shot  G  ducks  on  Monday,  and  11  on 
Wednesday ;  how  many  did  he  shoot  on  both  days  ? 

8.  He  used  on  Monday  2  pounds  of  duck-shot,  and  on 
Wednesday  5  pounds ;  how  many  pounds  did  he  use  in 
all? 

9.  The  5  pounds  of  shot  cost  him  6  shillings,  and  the 
2  pounds  were  given  him ;  how  much  did  the  shot  cost 
him? 

10.  If  you  pay  9  cents  for  some  sewing-silk,  and  ten 
cents  for  some  tape,  how  many  cents  do  you  pay  for  both? 

11.  If  you  buy  six  cakes  of  one  man,  and  eleven  of 
another,  how  many  cakes  do  you  buy  of  both  ? 

12.  There  are  6  apples  on  one  tree,  and  19  on  an- 
other ;  how  many  on  both  ? 

13.  On  one  shelf  there  are  6  books,  on  another  7;  how 
many  on  both  ? 

14.  Susan  received  from  her  mother  6  cents  at  Thanks- 
giving, and  1 1   cents  at  Christmas ;  how  many  cents  did 
she  receive  in  all  ? 

15.  Edna's  book  has  8  pictures,  and  Eudora's  has  6; 
how  many  pictures  have  both  books? 

16.  John  has  been  punished  6   times  at  school,  and  8 
times  at  home ;  how  many  times  has  he  been  punished 
in  all? 


ADDITION.  23 

LESSON  XXI. 
WRITTEN  EXERCISES. 

f!24)    (125)    (126)    (127)  (128)  (129) 

13412  41324  41321  51321  32132  51324 

46712  62132  35326  41324  46213  42676 

35273  41653  45624  41324  24132  25014 

24134  25625  52334  50604  36213  30629 

45652  32134  41302  60621  41621  46532 

35213  43253  10343  40132  41321  42624 


(130)  (131)  (132)  (133)  (134)  (135) 

43562  34160  30123  32141  41324  41032 

41324  45602  40621  32460  104  41011 

63260  45032  30423  1403  3  10 

41306  60324  40162  210  4107  2 

40160  40432  30152  12  06  6721 

24143  40162  15216  30  2  3 


LESSON  XXII. 

(136)    (137)  (138)  (139)  (140)  (141) 

41324  41324  41321  32592  41324  41321 

34120  16213  62162  31416  30143  41032 

60462  40123  42342  20413  62143  40162 

30621  30623  62103  40162  40132  32162 

41032  43216  66552  41324  40110  41314 

41621  21432  45625  51602  62162  62132 


(142)  (143)  (144)  (145)  ^146)  (147) 

13241  41322  41326  41332  13141  35213 

32162  46213  45324  46213  32625  41321 

46213  41362  35621  34213  32413  32319 

41023  65215  51212  34320  65252  20130 

54136  41352  34162  62133  35324  46050 

21036  24162  30130  14120  34521  40650 


u 


ADDITION. 


1  and  7  are     8. 
2  and  7  are     9. 
3  and  7  are  10. 

LESSON   XXIII. 
TABLE. 

4  and  7  are  11. 
5  and  7  are  12 
8  and  7  are  13. 

7  and  7  are  14. 
8  and  7  are  15. 
9  and  7  are  Jg] 

?  Exercise. 

11  +  7  =  ?  12  +  7  =  ?   13  +  7=?  14  +  7=?  efc. 

20  +  7=?  21+7=?  22  +  7  =  ?  23  +  7  =  ?  24  +  7  =  ?  etc. 

30+7  =  ?  31+7  =  ?  32  +  7=?  33  +  7  =  ?  34  +  7=?  etc. 

40  +  7  =  ?  41+7=?  42+7=?  43  +  7  =  ?  44  +  7  =  ?  etc. 

50  +  7  =  ?  51+7=?  52  +  7=?  53  +  7  =  ?  54  +  7  =  ?  etc. 

etc.  etc.                etc.                etc. 


etc. 


BLACKBOARD  EXERCISES. 


(1) 

01724 

77777 


(2) 

36598 

77777 


(3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

cJcciocJoceJ 
<g<g<g<34d*4.  «8 

77777777 
77777772 
77777777 
77777773 
77777772 
77777773 
77777772 
71234561 


LESSON  XXIV. 
MENTAL  EXERCISES. 

1.  Olive  gave  7  cents  for  a  slate,  and  3  cents  for  a 
pencil ;  how  much  did  she  give  for  both  ? 

2.  Melissa  bought  an  orange  for  4  cents,  and  some 
plums  for  7  cents ;   how  many  cents  did  she  give  for 
both? 

3.  Jane  gave  7  cents  for  tape,  and  10  cents  for  nee- 
dles ;  how  many  cents  did  she  give  for  both  ? 


ADDITION. 


25 


4.  Samuel  bought  some  wafers  for  7  cents,  and  some 
steel  pens  for  1 1  cents ;  how  many  cents  did  both  cost 
him? 

5.  Alexander  bought  a  slate  for  12  cents,  and  a  sponge 
for  7  cents ;  how  much  did  he  give  for  both? 

6.  Mary  paid  7  cents  for  some  muslin,  and  nine  cents 
for  some  gingham ;  what  did  she  pay  for  both  ? 

7.  James  earned  by  picking  cherries,  7  cents  the  first 
day,  and  1 1  cents  the  next  day ;  how  much  did  he  earn 
in  both  days  ? 

8.  What  must  I  pay  for  having  two  errands  done,  if  I 
give  7  cents  for  the  iirst,  and  9  cents  for  the  second  ? 

9.  Kate  had  a  bouquet  of  7  roses,  and  Mary  one  of  1 1 
roses ;  how  many  roses  in  both  bouquets  ? 

10.  It  rained  eleven  times  one  month,  and  7   times 
the  next ;  how  many  times  did  it  rain  during  the  two 
months  ? 

11.  Six  boys  and  7  girls  were  picking  berries  in  a 
pasture ;  how  many  children  were  there  in  all  ? 

LESSON  xxv. 
WRITTEN  EXERCISES. 


(148) 

(149) 

(15.0) 

(151) 

(152) 

(1S3) 

34106 

37103 

41321 

34132 

4132 

37012 

70132 

60123 

60723 

40621 

7642 

37012 

10716 

70172 

40162 

70162 

7017 

16021 

41307 

40130 

037 

43216 

3712 

30412 

62132 

62532 

4013 

21701 

6072 

52352 

41621 

41670 

41 

30721 

4170 

62132 

ADDITION. 


(154) 

(155) 

(156) 

(157) 

(158) 

(159) 

5232 

41321 

32134 

413212 

3121 

37124 

4013 

60213 

2234-3 

413216 

4137 

34135 

6217 

41G02 

40262 

413210 

5702 

25312 

3017 

41321 

32163 

465271 

3562 

40352 

1472 

42321 

41323 

617172 

5213 

70712 

1213 

41621 

41621 

312711 

4134 

34372 

LESSON 

XXVI. 

(160) 

(161) 

(162) 

<163) 

(164) 

(105) 

52132 

41324 

13416 

3 

71344 

14137 

41306 

32162 

2134 

4 

34121 

14216 

32732 

40216 

413 

682 

36214 

18214 

41362 

15723 

24 

4137 

56772 

32724 

41321 

41321 

1 

14 

46132 

34162 

34162 

01321 

6712 

31 

41613 

13713 

1  >6.  A  boy  spant  463  cents  for  a  coat,  and  1149 
cants  for  a  pair  of  pants  and  boots ;  how  much  did  he 
spend  for  all  ? 

1H7.  A.  T.  Stewart  paid  93680  dollars  for  a  store, 
and  118210  dollars  for  goods  ;  what  did  both  cost  him  ? 

168.  In  a  barrel  there  are  519  apples;   in  a  box  there 
are  1477  apples;   how  many  in  both  ? 

169.  There  are  710  nuts  in  one  pile,  in  a  second  there 
are  1555  more   than  in  the  first ;   how  many  Luts  in  the 
Bscond  pile  ? 

170.  A  boy  had    137  cents  in  his  pocket ;  his  father 
gave  him  85  cents  more ;    how  many  had  he  then  ? 

171.  Surnuel  had  1964  cents  in   a  savings  bank;  he 
afterward  put  in  1176   more  ;   how  much  had  he  then  in 
the  bank  ? 


ADDITION. 


27 


LESSON    XXVII. 

TABLE. 

1  and  8  are  9. 
2  and  8  are  10. 
3  and  8  are  H. 

4  and  8  are  12. 
5  and  8  are  13. 
6  and  8  are  14. 

7  and  8  are  15. 
8  and  8  are  16. 
9  and  8  are  17. 

Table  Exercise. 

h  8  =  ?  11+8  = 
-8-=?  21'+  8  = 

?   12  +  8=?    13  +  8  =  ?   14  +  8  = 
?   22+8=?  23  +  8  =  ?  24+8  =  ? 

10 


30  +  8  =  ?  31  +  8  =  ?  32  +  8  =  ?   33  +  8  =  ?  34  +  8  =  ?  etc. 

40  +  8  =  ?  41  +  8  =  ?  42  +  8  =  ?  48  +  8  =  ?  44  +  8  =  ?  etc. 

60  +  8  =  ?  51  +  8  =  ?  52  +  8  =  ?   53  +  8  =  ?  54  +  8  =  ?  etc. 

etc.                 etc.  etc.  etc. 


etc. 


BLACKBOARD  EXERCISES. 


(1) 

18729 


(21 

63054 
88888 


(3)   (4)   (5)   (6)   (7)   (8)   (9)  (If)  (11) 

«3  O  O  CJ  O  O  O  W  « 

c^^^c^c^^c^^^ 

888888883 
888888885 
888888882 
888888887 
888888888 
888888883 
888888887 
812345G72 


LESSON  XXVIII. 
MENTAL  EXERCISES. 

1.  If  you  place  8  books  in  one  pile,  and  8  in  another, 
Iiow  many  books  will  there  be  in  both  piles  ? 

2.  There  are  8  roses  in  blossom  on  one  bush,  and  teu 
on  another ;  how  many  on  both  ? 

3.  There  are  eight  pinks  in  blossom  from  one  root,  and 
9  from  another ;  how  many  from  both  roots  ? 

4.  There  are  8  bircls'-nests  in  one  grove,  and  eight  in 
unolher ;  how  many  nests  in  both  groves  ? 


20  ADDITION. 

5.  If  I  buy  2  barrels  of  flour  for  8  dollars,  and  1  ban 
rel  of    sugar  for   12   dollars,  how   much    will  my  bill 
amount  to  ? 

6.  I  bought  3  straw  liats  of  one  man  for  2  dollars,  and 
8  of  another  for  eight  dollars;  how  much  did  my  hats 
cost  me  ? 

7.  There  are  five  huts  in  one  row,  and  eight  in  an- 
other; how  many  huts  in  both  rows? 

8.  How  many  are  14  and  six  ?    24  and  6  ?    34  and  6  ? 
44  and  6?    54  and  6?    64  and  6?   74  and  6?    84  and  6? 
94  and  6?    How  many  are  3  and  8  ?  13  and  8?  23  and  8? 
33  and  8?    43  and  8?    53  and  8?    63  and  8?    73  and  8? 
83  and  8?    93  and  8? 

9.  Count  from  100  to  10;  thus,  100,  90,  80,  70,  &c. 
10.  Count  from  20  to  1 ;  thus,  20,  19,  18,  17,  16,  &c. 


LESSON 

XXIX. 

WRITTEN  EXERCISES. 

(172) 

(173) 

(174) 

(175) 

(176) 

(177) 

818764 

41342 

21341 

41832 

41372 

41783 

413721 

48324 

62437 

41672 

47726 

47867 

340272 

78772 

24167 

32171 

68783 

87716 

187642 

46724 

82416 

42313 

27167 

37872 

312413 

37862 

37137 

57717 

27178 

47132 

613752 

41371 

41683 

87671 

37183 

41367 

(178) 

(170) 

(180) 

(18!) 

(182) 

(183) 

41371 

641371 

413721 

81713 

4132 

41320 

21341 

407872 

671342 

41871 

8718 

71073 

31241 

868372 

413721 

24168 

3416 

04871 

67123 

413783 

671832 

37087 

8767 

67871 

47201 

413782 

878303 

89168 

4787 

70783 

78788  ' 

487213 

417832 

37168 

4607 

83782 

ADDITION.  29 

LESSON  XXX. 

(184)         (185)  (186)  (187)  (188)  (189) 

41340  41837  41372  41672  41834  41837 

21347  68773  46837  37183  67832  41678 

76827  41701  46713  63784  41786  38678 

48372  37456  48783  32487  67138  32168 

48372  75671  67187  67137  41687  41767 

41671  38716  38147  47183  48371  89168 

(190)  (191)  (192)  (193)    (194)  (195) 

41071  13716  41371  41372  71324  41674 

60872  41372  62710  48637  67168  34187 

41876  67187  04701  24873  32417  62184 

86716  47183  37124  21437  63418  67132 

40713  86713  37672  67138  46728  48667 

87241  46713  48372  63418  87832  47183 


LESSON  XXXI. 

(196)    (197)  (198)    (199)   (200)   (201) 

67123  41374  41371  41372  3467  41314 

41670  21367  21413  41672  4137  67183 

37087  41321  61783  40132  6718  28372 

86707  61713  87167  67104  7876  67027 

(202)  (203)  (204)  (2CO)   (206)   (207)   (208)  (209) 

413  413  613  312  4167  4137  312  456 

671  271  714  417  8723  6123  417  471 

387  687  834  807  7167  4167  686  657 

216  348  318  603  4168  4137  607  456 

417  483  772  477  3718  6718  807  432 

317  876  837  288  6167  3712  711  467 

213  417  617  678  4137  6137  707  338 

621  412  416  372  6874  2162  160  786 


30  ADDITION. 


LESSON    XXXII. 

TABLE. 

1  and 

9 

are 

10. 

4  and  9  are 

13. 

7 

and 

9 

are 

16 

2  and 

9 

are 

11. 

5  and  9  are 

14. 

8 

and 

9 

are 

17! 

3  and 

9 

are 

12. 

(5  and  9  are 

15. 

9 

and 

9 

are 

18. 

Table  Exercise. 

10  +  9=?  11+9=?   12  +  9=?  13+9  =  ?  14  +  9=?  etc. 

20  +  9=?  21  +  9  =?   22  +  9  =?  23  +  9  =  ?  24-j-9  =  ?  etc. 

3  )  +  9  =  ?  31  +  9  =  ?   32  +  9  =  ?  33  +  9  =  ?  34 -f  9  =  ?  etc. 

40  4-9=?  41+9=?   42  +  9=?  43+9  =  ?  44  +  9  =  ?  etc. 

50  +  9  =  ?  51  +  9  =  ?   52  +  9  =  ?  53  +  9  =  ?  54  +  9  =  ?  etc. 
etc.                 etc.                 etc.                 etc.  etc. 

BLACKBOARD   EXERCISES. 

(3)   (4)   (Z)   (6)   (7)   (8)   (9)  (10) (11)  (12| 

/i\  ododooeJsJdo 

W  <3<3<3c3<3<£43<3<3<!3 

192849999999999 

9999-99999999993 

-----9999999997 

9999999992 

(2)       9999999993 

730659999999996 

999999999999994 

-----9123456785 


LESSON  XXXIII. 
MENTAL  EXERCISES. 

1.  It  cost  9  dollars  to  get  my  sleigh  repaired,  arid  tf 
dollars  to  buy  a  new  harness ;  how  much  did  I  spend  ? 

2.  Charles  saw  9   ducks  in  one  flock,  and  11   in  an- 
other ;  how  many  ducks  did  he  see  in  all  ? 

3.  Julius  gathered  10  quarts  of  chestnuts  in  one  day, 
and  his  brother  gathered  9 ;  how  many  quarts  did  both 
gather  ? 


ADDITION. 


31 


4.  There  are  9  pigeons  in  one  flock,  and  6  in  another  ; 
how  many  pigeons  in  both  flocks  ? 

5.  There  are  4 "workmen  in  one   shop,  and  7  in  an- 
other ;  how  many  workmen  in  both  ? 

6.  If  a  farmer  has  9   cows  in  a  field,  and  puts  in  7 
more,  how  many  will  he  then  have  in  the  field  ? 

7.  There  are  3  rabbits  in  the  cage,  and  5  in  the  gar- 
den ;  how  many  are  there  in  all  ? 

8.  If  Charles  has  two  notes  due  him,  one  for  7  dollars, 
and  the  other  for  8  dollars,  how  much  is  due  him  in  all  ? 

9.  James  has  8  sheep  and  2  lambs ;  how  many  has  he 
of  both  ? 

LESSON  XXXIV. 

WRITTEN  EXERCISES. 

(210)          (211)         (212)         (213)          (214)        (215> 

41372  96876  91876  61783  41978  4786 

60241  41878  49837  91876  39838  4983 

78978  37418  49183  41983  78768  9778 

64138  67183  49703  87678  71867  6718 


(216)  (217)  (218)  (219)  (220)  (221) 

41372  34187  3876  98712  41837  41873 

91671  86783  4137  64134  68321  41678 

48783  91671  9413  37867  41671  98783 

91678  49871  7681  91837  89672  24167 


(222)  ~   (223)  (224)  (225)  (226)  (227) 

37164  41672  41983  91876  83716  41839 

18716  48786  87683  41983  49896  67187 

91876  97898  91787  71867  49837  91837 

80713  39876  64183  41919  89168  86784 


32  ADDITION. 

LESSON   XXXV. 

228.  1203  apples   are  worth  957  cents,  530  oranges 
are  worth  1709  cents;  how  much  are  both  worth  ? 

229.  57  bushels  of  potatoes  are  worth  120  dollars,  and 
some  beets  are  worth  118  dollars,  what  are  both  worth  ? 

230.  There  are  three  barrels  of  potatoes,  the  first  is 
worth   320  cents,  the  second  287  cents,  and  the  third 
worth  795  cents;  what  is  the  value  of  all? 

231.  A  box  contains  137  oranges  and  a  barrel  contains 
85  more  than  the  box ;  how  many  oranges  in  the  barrel  ? 

232.  A  boy  placed  56  nuts  in  a  pile ;  how  many  nuts 
in  four  such  piles  ? 

233.  How  much  are  4  horses  worth  if  each  horse  is 
worth  400  dollars  ? 

234.  1340  arithmetics  cost  18680  cents;   1470  slates 
cost  6461  cents  ;  what  is  the  cost  of  both  ? 

235.  Eighty  bushels  of  wheat  cost  160  dollars  and 
100  bushels  of  rye  cost  sixty-seven  dollars  more  than 
the  wheat ;  what  did  the  rye  cost  ? 

236.  There  are  two  carts  in  the  street,  one  contains 
130  quarts  of  corn,  and  the  other  179  quarts  of  pota- 
toes ;  how  many  quarts  in  both  ? 

237.  There  are  53  boys  in  a  class ;  if  one  boy  has  23 
cents    and   another  boy  seven  cents,    how  many  cents 
have  both  boys  ? 

238.  John    has  230  marbles,  Marvin  has   75    more 
than  John;  how  many  marbles  has  Marvin  ? 

239.  Susan  had  1460  pins,  and  she  bought  2464  pins 
more ;  how  many  pins  had  she  in  all  ? 


SECTION   III. 
LESSON    I. 

1.  If  I  take  2  gallons  of  oil  from  4  gallons,  how  mucli 
"will  remain? 

FORMULA. — If  from  4  gallons  I  take  2  gallons,  there  will  remain  the 
cliflbrence  between  4  gallons  and  2  gallons,  which  is  2  gallons;  tben- 
fore  there  will  be  2  gallons  left. 

2.  If  John  has  three  marbles,  and  lose  one,  how  many 
has  he  then  ? 


34  SUBTRACTION. 

3.  Edwin  recited  4  lessons,  but  one  of.  them  was  im- 
perfect ;  how  many  perfect  lessons  did  he  recite  ? 

4.  Susan  was  bringing  home  6  cakes,  but  she  gave  one 
to  a  poor  boy ;  how  many  did  she  bring  home  ? 

5.  There  were  8  clothes-pins  in  the  basket,  and  Jane 
fastened  one  on  the  line ;  how  many  remained  in  the 
basket? 

6.  A  drover  bought  9  sheep,  and  sold  one ;  how  many 
remained  unsold  ? 

7.  A  boy  bought  7  marbles,  but  lost  one ;  how  many 
had  he  left  ?- 

8.  Charles  bought  8  peaches,  and  gave  one  away ;  how 
many  had  he  left  ? 

9.  Ella  had  5  pins  on  a  paper,  she  gave  one  to  Julia; 
how  many  had  she  left? 

10.  Lelia  had  10  peaches  given  her  by  her  uncle,  she 
gave  her  mother  one ;  how  many  had  she  left  ? 

11.  A  boy  gave  a  ten-cent-piece  to  pay  for  a  stick  of 
candy  that  cost  one   cent;    how  much  change  did  he 
receive  ? 

12.  There  were   7   potatoes  on  the  dish  at  dinner; 
Mary  took  one ;  how  many  remained  ? 

13.  Charles  caught  5  squirrels,  but  one  escaped ;  how 
many  had  he  left  ? 

14.  Henry  caught  9  nice  fish,  but  the  largest  escaped 
into  the  water ;  how  many  had  he  to  take  home  ? 

15.  Joseph  bought  a  melon,  but  on  going  home  a  larger 
boy  took  it  away  from  him;  how  many  had  he  when  he 
arrived  home  ? 


SUBTRACTION.  35 

LESSON  III. 

•WRITTEN  EXERCISES, 

In  which  each  figure  of  the  Minuend  is  ^qual  to  or  larger  than 
the  corresponding  figure  of  the  Subtrahend. 

(1)          (2)          (3)  (4)  (5)  (6)  (7)          (8) 

7689  3712  4134  3412  4167  1021  3417  1216 
1111  1111  1111  1111  1111  1011  1111  1111 


(9)    (10)    (11)    (12)    (13)    (14)    (15)    (.16) 

4167  3708  4167  4183  4134  6712  4137  4186 
1111  1101  1111  1011  1111  1011  1111  1011 


(17)    (18)    (19)    (20)    (21)    (22)    (23)    (24) 
8718  6891  3718  6975  4987  6913  4187  6213 
1111  1011  1001  1111  2101  1011  1011  1111 


LESSON  IV. 

.(25)   (26)    (27)    (28)    (29)  (30)  (31)  (32) 

9187  6413  9187  6542  4187  6834  7173  6712 

1111  1001  1111  1111  1111  1111  0110  1111 


(33)  (34)  (35)  (36)  (37)  (38)  (39)  (40) 
9837  8674  4187  8916  7834  9176  4137  2141 
1101  1101  1111  1011  1011  1101  1111  1111 


(41)    (42)    (43)    (44)    (45)    (46)    (47)    (48) 

1876  4137  8916  4183  7684  3416  8913  2186 
1111  1011  1101  1111  1111  1011  1011  1110 


*  NOTE  FOR  THE  TEACHER  —  The-teacher  may  instruct  the  pupil  in  the  method 
of  subtracting,  and  of  definitions,  &c.,  as  fully  as  he  may  deem  expedient. 
This,  probably,  can  best  be  done  by  oral  instruction  The  author's  object  is  to 
AID  the  teacher,  by  giving  systematically  graded  examples  for  practice. 


33 


SUBTRACTION. 


LESSON   V. 

TABLE. 

1 

from 

1 

leaves 

0. 

2 

from 

2 

leaves 

0. 

1 

from 

2 

leaves 

1. 

2 

from 

3 

leaves 

1 

from 

3 

loaves 

2. 

2 

from 

4 

leaves 

2. 

1 

fro  .11 

4 

leaves 

3. 

2 

from 

5 

leaves 

3. 

1 

from 

5 

leaves 

4. 

2 

from 

6 

leaves 

4. 

1 

from 

6 

leaves 

5. 

2 

from 

7 

leaves 

5. 

1 

from 

7 

leaves 

6. 

2 

from 

8 

leaves 

6- 

1 

from 

8 

leaves 

7. 

2 

from 

9 

leaves 

7. 

1 

from 

9 

leaves 

8. 

2 

from 

10 

leaves 

8. 

1 

from 

10 

leaves 

9, 

2 

from 

11 

leaves 

9, 

BLACKBOARD   EXERCISES. 

(1) 

11     10       2       9       3       8       4       7 
22222222 


11     18     19     20 
2       2       22 


12     17     13     16     14     15 
222222 


(3) 

21     27     28     22     26     23     29     25     24     30 
2222222222 


NOTE.— These  exercises  are  to  be  recited  in  the  same  manner  as  similar  exer- 
eises  preceding. 

LESSON   VI. 
MENTAL  EXERCISES. 

1.  A  boy  had  3  marbles  in  his  pocket,  but  two  dropped 
out  through  a  hole  ;  how  many  marbles  had  he  left? 

SOLUTION. — The  solution  is  the  same  as  in  Lesson  II. 

2.  Charles  bought  5  pencils,  and  lost  2 ;  how  many 
had  he  left? 


SUBTRACTION.  37 

3.  Ada  found  6  cents,  but  afterwards  lost  2  of  them ; 
how  many  had  she  remaining? 

4.  Annette  bought  a  book  for  8  cents,  and  gave  the 
clerk  a  ten-cent  piece ;    how  much    change  should  she 
receive  ? 

5.  There  were  9  robins  stealing  cherries;  John  shot 
2,  the  rest  flew  away ;  how  many  were  unhurt  ? 

6.  Eight  boys  started  to  ride  down  a  hill  on  a  sled,  but 
2  fell  off;  how  many  were  on  the  sled  at  the  bottom  of 
the  hill? 

7.  From  a  rake  that  had  4  teeth,  Charles  broke  out 
two ;  how  many  were  left  ? 

8.  A  lad,  in  climbing  a  steep  bank,  gained  5  yards  and 
fell  back  2  yards  each  minute ;  how  many  yards  did  he 
gain  each  minute  ? 

9.  There  were  8  persons  in  a  railroad  car ;  two  got 
out ;  how  many  remained  ? 

10.  Sarah  has   7  pins,  and  Julia  has  2 ;  how  many 
more  pins  has  Sarah  than  Julia? 

11.  John  caught  9  fish,  Henry  caught  2  ;  how  manj 
fish  did  John  catch  more  than  Henry  ? 

12.  If,  of  7  lights  in  a  street,  two  are  blown  out,  how 
many  will  be  left  burning  ? 

13.  Harry  recited   11    lessons,  Julius  2;  how  many 
more  lessons  did  Harry  recite  than  Julius  ? 

14.  A  man  drove  9  horses  to  market,  and  sold  2  ;  how 
many  were  unsold  ? 

15.  A  poor  boy  bought  4  boxes  of  matches,  but  could 
wily  sell  2  ;  how  many  boxes  remained  unsold  ? 


68 


SUBTRACTION. 


LESSON   VII. 
WRITTEN  EXERCISES. 

(49)  (50)          (51)         (52)          (58)  (54)  (55) 

87186  41868  3784  9168  34186  41872  4167 
11011  11101  1101  1012  12102  21021  1021 


(56)    (57)    (58)    (59)    (60)     (61)     (62) 

67134  4167  4186  4108  71864  37188  4123 
11012  2122  2102  2102  21221  12122  2122 


(63)    (64)    (65)    (66)    (67)    (68)     (69) 

9187  6413  9871  4167  8768  31214  416758 
1102  2210  2020  1222  2121  21214  412222 


LESSON  VIII. 

(70)     (71)     (72)    (73)  (74)  (75) 

41674  87162  98374  16783  91246  91234 

11222  22121  12212  10221  21211  21211 


(76)     (77)     (78)     (79)    (SO)    (81) 
41674  37412  '67123  41374  21672  41876 
10111  12202  32122  20232  21321  20301 


(82)     (83)     (84)     (85)     (86)     (87) 
41262  41324  36241  41372  41372  41372 
21221  zi211  22121  21221  21221  21222 


SUBTRACTION. 


39 


3  from  4  leaves  1. 
3  from  5  leaves  2. 
3  from  6  leaves  3. 

10  +  3  =  ?  11  +  3: 
10  —  3  =  ?  11  —  3  : 
20  +  3  =  ?  21  +  3: 
20  —  3  =  ?  21  —  3: 
30  +  3  =  ?  31  +  3  i 
30  —  3  =  ?  31  — 3  i 
etc.  etc. 


LESSON    IX. 

TABLE.* 

3  from  7  leaves  4.  3  from  10  leaves  7. 
3  from  8  leaves  5,  3  from  H  leaves  §! 
3  from  9  leaves  (>.  3  from  12  leaves  0] 

Table  Exercise. 

:  ?  12  -f  3  =  ?  13  +  3  =  ?  14  +  3  =  ?  etc. 
:?  12-3=?  13-3=?  14-3=?  e'.c. 
:  ?  22  -f-  3  =  ?  23  +  3  =  ?  24  +  3  =  ?  etc. 
:  ?  22  —  3  =  ?  23  —  3  =  ?  24  —  3  =  ?  etc. 
:  ?  32  +  3  =  ?  33  +  3  =  ?  34  -f  3  =  ?  etc. 
:?  32  —  3=?  33  —  3  =  ?  34  —  3  =  ?  etc. 
etc.  etc.  etc. 


BLACKBOARD    EXERCISES. 
(1) 

3     11       4     10       5       96       7 
33333333 


8     12 
3       3 


13     19     14     18     15     20     16     21     17     22 
3333333333 

(3) 

23  30  32  24  31  29  25  27  26  28 
3   3   3   3   3   333   3   3 


•       LESSON  X. 
MENTAL  EXERCISES. 

1.  If  you  buy  4  cakes  for  your  lunch,  and  on  your 
way  to  school  lose  3,  how  many  will  you  have  left? 

2.  If  you   buy   5  slate-pencils,  and  you  lose  3,  how 
many  will  you  have  left? 

•  NOTE  FOR  THE  TEACHER  —The  teacher  should  net  neglect  to  question  the 
pupils  thoroughly  and  repeatedly  on  the  table 


40  SUBTRACTION. 

3.  Samuel  placed  7  peaches  on  the  table  for  his  mother, 
but  his  brother  took  away  3  ;  how  many  were  left  ? 

4.  There  were  9  apples  on  the  table,  and  Mary  hid  3 
of  them  ;  how  many  remained? 

5.  There  were  11  pears  on  a  plate,  and  Horace  ate  3 
of  them ;  how  many  were  left  ? 

6.  If  you  cut  off  3  feet  from  a  string  13  feet  long, 
how  much  will  be  left  ? 

7.  A  boy  bought  a  large  kite  for  12  cents,  and  then 
sold  it  for  3  cents  less  than  he  gave  for  it ;  how  much  did 
he  receive  for  it  ? 

8.  John  bought  a  book  for  15  cents,  and  sold  it  for  3 
cents  less  than   he  gave  for  it ;  for  how  much  did  he 
sell  it  ? 

9.  I  bought  a  pig  for  9  dollars,  and  sold  it  for  3  dollars 
less  than  I  gave  for  it ;  how  much  did  I  receive  for  it  ? 

10.  There  were  1 1  cows  in  the  pasture,  and  a  boy  drove 
out  3 ;  how  many  remained  ? 

11.  A  drover  had  19  horses,  and  sold  all  except  3-, 
how  many  did  he  sell  ? 

12.  A  boy  had  17  marbles,  but  in  playing  he  lost  all 
but  3 ;  how  many  marbles  did  he  lose  ? 

13.  Henry  caught  5  fishes,  and  the  cat  stole  3 ;  how 
many  had  he  left  ? 

14.  Charles  picked  7  bushels  of  pears,  and  George 
picked  as  many  lacking  3 ;  how  many  did  George  pick  ? 

15.  Thomas  owns  13  sheep,  his  brother  James  has  as 
many  lacking  3  ;  how  many  has  James  ? 


SUBTRACTION.  < 

LESSON  XI. 
WRITTEN  EXERCISES. 

(88)  (89)  (90)  (91)  (92)  (93) 

418764     41374     86712     91876     41034     68712 
113232     31232     33212     31213     21032     32112 


(94)     (95)     (96)     (97)     (98)     (99) 

91871  6713  98712  61713  98173  67121 
20331  3213  33311  30303  32032  31121 


(100)    (101)    (102)     (103)     (104)    (105) 

41876  38789  64187  918764  187137  69123 
31023  13321  33123  312311  123013  32122 


LESSON  XII. 

(106)     (107)    (108)    (109)  (110)  (111) 

418764  13912  67134  67183  91276  41876 

213321  13311  32132  21033  21230  31232 


(112)    (113)    (114)    (115)    (116)    (117) 

41876  41837  68346  41264  43418  67134 
20321  31231  32311  31232  33213  31132 


(118)    (119)    (120)    (121)    (122)    (123) 

43786  41873  91674  87183  69134  87186 
22342  21323  31233  23132  33132  32132 


SUBTRACTION. 


4  from  5  leaves  1. 
4  from  6  leaves  2. 
4  from  7  leaves  3. 

104-4  =  ?  11  +  4 
lo_4  —  9  11  —4 

20  +  4  =  ?  21+4; 
20  —  4  =  ?  21—4 
30  +  4  =  ?  31  +4 
30  —  4  =  ?  31—4 
etc.  e!c. 


LESSON   XII. 

TABLE. 

4  from  8  leaves  4.  4  from  1 1  leaves  7. 
4  from  9  leaves  5.  4  from  12  leaves  8 
4  from  10  leaves  6.  4  from  13  leaves  9, 

Table  jEJxercise. 

=  ?  12+4=?  13  +  4  =  ?  14  4-4  =  ?  <tfc. 
=  ?  12  —  4=?  13-4  =  ?  14-4  =  ?  etc. 
=  ?  22  +  4=?  23  +  4  =  ?  24  +  4  =  ?  efc. 
=  ?  22  —  4=?  23  —  4  =  ?  24  —  4  =  ?  etc. 
3?  32  +  4  =  ?  33+4  =  ?  34  +  4  =  ?  etc. 
=  ?  32  —  4  =  ?  33  —  4  =  ?  34  —  4  =  ?  etc. 
etc.  etc.  etc. 


BLACKBOARD     EXERCISES 


5     11 

4       4 


(1) 

6     12     10 
444 


7 
4 


8     13 
4       4 


(2) 

14     22     16     15     17     23     21     18     20     19 
4444444444 


(3) 

24     33     25     32     26     31     27     30     28     29 
4444444444 


LESSON    XIV. 
MENTAL  EXERCISES. 

1.  If  you  have  7  quarts  of  milk  in  a  pail,  and  you 
spill  4  quarts,  how  many  quarts  remain  ? 

2.  If  you  play   6  games  of  ball,  and  are  beaten  in  4 
games,  in  how  many  games  are  you  not  beaten  ? 


SUBTRACTION.  43 

• 

3.  There  are  11  lines  to  be  written  in  your  writing- 
book  ;  you  have  written  all  but  4 ;  how  many  lines  have 
you  written  ? 

4.  A  beggar-man  had  8  cents  given  him ;  he  spent  4 
for  bread ;  how  many  cents  had  he  remaining  ? 

5.  There  are  7  days  in  a  week,  and  if  you  are  sick  4 
days,  how  many  days  are  you  well  ? 

6.  Nora  had  5  new  dresses  in  a  year ;  she  wore  out 
4  of  them;  how  many  ha(J  she  left? 

7.  There  are  13  bricks  in  one  pile,  and  as  many  in  *, 
second  pile  lacking  4 ;  how  many  bricks  in  the  second 
pile? 

8.  There  are  18  leaves  in  a  book;  if  you  tear  out  4 
?f  them,  how  many  will  remain  ? 

9.  John  bought  a  little  wagon  for  6  dollars,  and  then 
sold  it  for  4  dollars;  did  he  make,  or  lose,  and  how  much? 

10.  A  merchant  bought  13  yards  of  silk  for  15  dollars? 
6\it  it  being  damaged,  he  was  obliged  to^sell  it  for  4  dollars* 
less  than  it  cost  him ;  how  much  did  he  receive  for  it  ? 

11.  A  grocer  bought  some  sugar  for  7  dollars,  and  after' 
ward  sold  it  for  4  dollars ;  how  much  did  he  lose  ? 

12.  There  are  17  sheep  in  one  field,  and  as  many  in 
a  second  as  in  the  first,  lacking  4  sheep ;  how  many  sheep 
in  the  second  field? 

13.  Henry  is  13  years  old,  James  is  4  years  younger; 
how  old  is  James  ? 

14.  Susan  is  7  years  old,  Edna  is  4;  how  much  older 
is  Susan  than  Edna?  ^— •— 

15.  Carrington  solved   15  examples  in  Arithmetic;  4 
were  incorrect;  how  many  were  correct?  * 


44  SUBTRACTION. 

LESSON    XV. 
WRITTEN   EXERCISES. 

(124)    (125)    (126)    (127)    (128)    (129) 
48786  41837  89186  41832  91876  41896 
32132  41432  44141  31432  41342  41332 


(130)    (131)    (132)    (133)    (134)    (135) 

86413  41876  41834  67872  44186  91876 
34413  21421  21434  81432  40142  31442 


(136)    (137)    (138)    (139)    (140)    (141) 

91876  41987  68341  78374  86974  98786 
31343  21344  14041  32343  42434  41434 


LESSON  XVI. 

(142)    (143)    (144)    (145)  (146)  (147) 

91876  4187?  91670  49186  49187  41867 

31042  31403  41430  41143  44143  41324 


(148)    (149)    (150)    (151)    (152)    (153) 

91876  49187  67834  19187  67189  64183 
41432  24141  03421  14144  34124  32141 


(154)    (155)    (156)    (157)    (158)    (159) 

918761  41834  67183  91374  68014  91846 
414101  41231  32142  41244  13014  31441 


SUBTRACTION. 


LESSON    XVII. 


45 


5  from  6  leaves  1. 
5  from  7  leaves  2. 
5  from  8  leaves  3. 

5  from     9  ]  eaves  4. 
5  from  10  leaves  5. 
5  from  11  leaves  6, 

5  from  12  leaves  7. 
5  from  13  leaves  8. 
5  from  14  leaves  9. 

Table  Exercise. 

10  +  5=?    11  +  5  : 

10-5=?  11  —  5  : 

=  ?   12  4-  5  =?  13  +  5=?  14  +  5=?  etc, 
=  ?   12  —  5=?   13  —  5  =  ?  14  —  5  =  ?  etc. 

20+6  =  ?  21  +  5: 
20  -  5  =  ?  21  —  5  = 

=  ?   22  +  5  =?  23  +  5  =  ?  24  +  5  =  ?  etc. 
=  ?  22  —  5  =  ?  23  —  5  =  ?  24  —  5  =  ?  etc. 

30  +  5=?  31  +  5  i 
30  —  5  =  ?  31  —  5: 

=  ?   32  +  5  =  ?  33  +  5  =  ?  34  +  6  =  ?  etc. 
-  ?  32  —  -5  =  ?  33  —  5  =  ?  34  —  5  =  ?  etc. 

etc.               etc. 

etc.          •      etc. 

etc. 

BLACKBOARD  EXERCISES 

(1) 

5     13       6 

12       7     14       8 

11       9     10 

555 

5555 

555 

(2) 


15     24     16     18     17 
55555 


20     19     23     21     22 
55555 


(3) 

26     34     25     33     27     32     28     31     29     30 
5555555555 


LESSON    XVIII. 
MENTAL  EXERCISES. 

1.  There  were  9  plums  on  the  tree ;  Jacob  knocked 
off  5  ;  how  many  remained  on  the  tree  ? 

2.  Susan  had  1 1  pins  in  her  cushion ;  the  servant  took 
out  5  ;  how  many  remained  ? 


46  SUBTRACTION. 

3.  Ellen  performed  13  examples  in  Mental  Arithmetic, 
Nettie  performed  as  many  lacking  5 ;    how  many  did 
Nettie  perform  ? 

4.  The  teacher  gave  15  questions  to  the  class ;  5  were 
answered  correctly,  and  the  rest  incorrectly ;  how  many 
were  answered  incorrectly  ? 

5.  There  were  16  words  given  out  to  the  spelling-class  ;  • 
5  were  misspelled ;  how  many  were  spelled  correctly  ? 

6.  There  were  6  boys  sitting  on  a  bench ;  5  have  a 
recess ;  how  many  remain  on  the  bench  ? 

7.  A  stage  travels  9  miles  in  one  hour,  the  next  hour 
it  travels  as  many  miles  lacking  5  ;  how  many  miles  did 
the  stage  travel  the  last  hour  ? 

8.  There  were  9  persons  in  the  stage,  but  5  of  them  be- 
came tired  and  got  out ;  how  many  remained  in  the  stage  r 

9.  13  boys  started  for  school,  but  5  of  them  played 
truant  and  went  off  to  play;   how  many  arrived  at  the 
school  ? 

10.  George  had  14  marbles  when  he  commenced  play- 
ing with  James,  but  he  lost  all  but  5  ;   how  many  did  he 
lose? 

11.  His  14  marbles  cost  him  9  cents,  and  the  5  mar- 
bles which  he  had  left  he  sold  for  5  cents ;  how  many 
cents  did  his  game  cost  him  ? 

12.  If  I  have  16  quarters  of  an  apple,  and  give  away 
5  quarters,  how  many  quarters  will  I  have  left  ? 

13.  If  I  have  17  quarters  of  a  melon,  and  give  away 
5  quarters,  how  many  quarters  will  I  have  left? 

14.  If  I  have  9  halves  of  an  orange,  and  give  away  5 
halves,  how  many  halves  will  I  have  left  ? 


SUBTRACTION.  47 

LESSON    XIX. 

*  WRITTEN  EXERCISES, 

In  which  each  alternate  figure  of  the  Subtrahend  is  larger  than  the 
Corresponding  figure  of  the  Minuend. 

(160)  (161)  (162)  (163)  (164) 

927381  917183  618190  519080  924390 
345432  421354  234221  324121  432412 

(165)     (166)     (167)     (168)     (169) 

527082  816141  423453  732250  734271 
232154  135212  141514  241341  241342 

(170)     (171)     (172)     (173)     (174) 
826041  705180  537250  527382  827191 
434425  443544  243424  343424  134542 

LESSON  XX. 

(175)      (176)      (177)     '(178)      (179) 
92836171  72637051  52927341  82719143  74906181 
25245452  25352325  44532524  24154225  35442325 


(180)      (181)      (182)      (183)      (184) 

81918141  72927162  91735141  72534272  73804171 
24554434  43455345  34454223  45252354  48321334 


(185)      (186)      (187)      (188)      (189) 

93427391  42939081  61907282  72918051  61719273 
34142453  35252134  44411424  45544123  44453454 


*  NOTE  FOK  THE  TEACHER. — Before  the  pupil  is  lequired  to  perform 
the  following  exercises,  the  teacher  should  explain  the  method  of  sub- 
tracting when  the  figure  in  the  subtrahend  exceeds  the  corresponding 
figure  in  the  minuend.  (See  Introduction.) 


48 


SUBTRACTION. 


LESSON   XXI. 


6  from  7  leaves  1. 
6  from  8  leaves  2. 
6  from  9  leaves  3, 


6  from  10  leaves  4. 
6  from  11  leaves  5. 
(5  from  12  leaves  (J. 


6  frpm  13  leaves  7. 
6  from  14  leaves  8. 
6  from  15  leaves  9. 


10  +  6  =  ?  11+6 
10  —  6=?  11  —  6 
20  +  6  =  ?  21+6 
20—6=?  21  —  6 
30  +  6  =  :  31+6 
30  —  6  =  ?  31-6 
etc.  etc. 


Table  Exercise. 

=?  12  +  6=?  13  +  6  =  ?  14  +  6  =  ?  etc. 
=?  12—6=?  13  —  6  =  ?  14  —  6  =  ?  etc. 
=  ?  22  +  6  =?  23  +  6  =  ?  24  +  6  =  ?  etc. 
=  ?  22—6=?  23  —  6  =  ?24  —  6  =  ?  etc. 
=?  32  +  6  =  ?  33  +  6  =  ?  34  +  6  =  ?  etc. 
=?  32—6  =  ?  33  —  6=?  34  —  6  =  ?  etc. 
etc.  etc.  etc. 


6     13 
6       6 


BLACKBOARD 

EXERCISES. 

0) 

7 

12 

8 

11 

9 

14 

10 

15 

6 

6 

6 

6 

6 

6 

6 

6 

(2) 

25     18     17     16     20     19     22     21     24     23 
6666666666 


(3) 

26     28     27     35     29     32     33     31     34     30 
6666666666 


LESSON    XXII. 
MENTAL  EXERCISES. 

1.  There  were  7  pears  on  a  tree ;   Henry  knocked  off 
5  f  tow  many  remained  on  the  tree  ? 

2.  If  you  have  11   chestnuts  in  your  pocket,  and  you 
give  away  6,  how  many  will  you  have  left  ? 


SUBTRACTION.  49 

3    There  were  9  hop-poles  standing  in  a  row  ;  the  wind 
has  blown  0  oi  them  down;  how  many  remain  standing? 

4.  19  soldiers  went  into  battle,  but  G  of  them  proved 
towards  and  ran  away ;  how  many  remained  ? 

5.  8  ducks  were  brought  for  sale;   6  were  sold";  how 
many  remained  unsold  ? 

6.  Out  of  12  bushels  of  potatoes,  6  became  rotten ;  how 
many  bushels  remained  sound  ? 

7.  There  were  19  apples  on  a  tree,  and  Julius  knocked 
6  of  them  off;  how  many  remained? 

8.  A  man  bought  a  cow  for  19  dollars,  and  then  sold 
her  for  6  dollars  less  than   he  gave  for  her ;  how  much 
did  he  receive  ? 

9.  A  man  bought  14  baskets  of  peaches  for  12  dollars, 
and  then  sold  6  baskets  for  8  dollars ;  how  many  peaches 
had  he  left  ? 

10.  A  boy  had  13  marbles  in  his  desk;  his  brother 
took  out  6  ;  how  many  remained  ? 

11.  I  sold  a  set  of  chairs  for  16  dollars,  which  was  6 
dollars  more  than  they  cost  me ;  how  much  did  I  give  for 
them? 

12.  I  sold  12  sheep  for  18  dollars,  which  was  6  dollars 
more  than  they  cost  me ;  what  did  they  cost  ? 

13.  A  merchant  sold  9  pairs  of  shoes  for  12  dollars? 
which  was  6  dollars  more  than  he  gave  for  them ;  how 
much  did  he  give  for  them  ? 


50 


SUBTRACTION. 


LESSON  xxm. 


WRITTEN  EXERCISES. 

(190)               (191)               (192)               (193)  (194) 

92819171  61928271  92739192  71839171  92738292 

36243254  44230424  43250423  42343512  36562634 


(195)      (196)      (197)      (198)      (199) 

83918141  63707210  83728195  70729570  71806491 
45663432  45656301  24165216  36142631  32213652 


(200)      (201)      (202)      (203)      (204) 

91819180  72917371  72819073  83926171  91817182 
F5256251  24563453  43252134  34264213  44434643 


LESSON  XXIV. 

Exercises  in  which  each  figure  of  the  Subtrahend,  except  the  left 
hand  figure,  is  larger  than  the  corresponding  one  of  the  Minuend. 

(205)  (206)  (207)  (208)  (209) 

41111111  71111111  91111111  9222222  822222* 
14231256  23612456  24562122  3425433  442434* 


(210)      (211)      (212)      (213)      (214) 

6333333  8333333  6333333  9333333  8333333 

2453645  3456544  2334334  2333334  4333334 

(215)      (216)      (217)      (218)      (219) 

4333333  9333333  6333333  8333333  6333333 

2343434  2353535  2343434  6353535  2363636 


SUBTRACTION. 


51 


7  from  8  leaves  1. 
7  from  9  leaves  2. 
7  from.  10  leaves  3. 

10  4-7  =  ?  11  +  7: 
10-7  =  ?  11-7: 
204-7  =  ?  21+  7  - 
20-7  =  ?  21-7: 
30  +  7  =  ?  31  +  7  = 
30  —  7  =  ?  31  —  7: 
etc.  etc. 


LESSON    XXV. 

TABLE. 

7  from  1  1  leaves  4. 
7  from  12  leaves  5. 
7  from  13  leaves  6. 


JZ 


xercise. 


7  from  14  leaves  7. 
7  from  15  leaves  8. 
7  from  16  leaves  9. 


:?12+7  =  ?  13  +  7=?  14  +  7  =  ?  €fc. 
:  ?  12  —  7  =  ?  13  —  7  =  ?  14  —  7  =  ?  rtc. 
:  ?  22  4-  7  -  ?  23  +  7  =  ?  24  +  7=?  etc. 
:  ?  22  —  7  =  ?  23  —  7  =  ?  24  —  7  =  ?  efc. 
:  ?  32  +  7  =  ?  33  +  7  =  ?  34  4-  7  =  ?  «fc. 
:  ?  32  —  7  =  ?  33  —  7  =  ?  34  —  7  =  ?  efe. 


BLACKBOARD    EXERCISES. 


(1) 

8     10       9     12     11     16     17     15     14     13 

7777777777 


17     19     18     21     20     23     22     26     25     24 

7777777777 


(3) 

27     36     28  .  35     29     34     30     33     31     32 

7777777777 


LESSON  XXVI. 
MENTAL  EXERCISES. 

1.  Charles  gave  8  cents  to  William  and  7  cents  to 
James ;    how  many  more  did  he  give  to  William  than 
to  James  ? 

2.  A  man  gave  10  dollars  for  a  box  of  lemons,  and 


52  SUBTRACTION. 

7  dollars  for  a  box  of  oranges ;  how  many  more  dollars 
did  he  give  for  the  lemons  than  for  the  oranges  ? 

3.  A  farmer  brought  to  market  twelve  cheeses,  and 
sold  7  ;  how  many  remained  unsold  ? 

4.  A  merchant  sold  sugar  to  the  amount  of  1 1  dollars  ; 
he  received  7  dollars  down ;  how  much  was  then  due 
him? 

5.  I  paid  10  dollars  for  some  hay,  and  7  dollars  for 
some  straw ;  how  much  more  did  I  pay  for  the  hay  than 
for  the  straw  ? 

G.  A  boy  bought  a  book  for  1 6  cents,  and  a  slate  for  7 
cents ;  how  many  more  cents  did  he  pay  for  the  book  than 
for  the  slate  ? 

»  7.  Julia  bought  a  geography  for  25  cents,  and  some 
writing-paper  for  7  cents ;  how  much  more  did  the  geog- 
raphy cost  than  the  paper  ? 

8.  If  I  have   10  half-apples,  and  give  away  7,  how 
many  will  I  have  left  ? 

9.  John  had  13  quarters  of  an  apple  ;  he   gave  away 
7  ;  how  many  had  he  left? 

10.  There  are  10  tenths  in  an  apple;  if  I  give  away 
7  tenths,  how  many  tenths  will  remain  ? 

11.  There  are  19  nineteenths  in  an  apple;   if  7  nine- 
teenths are  taken  away,  how  many  will  remain  ? 

12.  There  are  20  twentieths  in  a  unit;  if  7  twentieths 
are  taken  away,  how  many  will  remain  ? 


SUBTRACTION. 


(220) 

4444444 
1484789 


LESSON  XXVII. 

WRITTEN  EXERCISES. 

(221)  (222)  (228) 


444444 
254749 


444444 
145789 


444444 
146476 


(224; 
444444 
144478 


(223)      (220)      (227)      (228)      (229) 

555555   555555   555555   555555   555555 
278589   455876   487768   387869   389788 


(2*0)      (231)      (232)      (233)      (234) 

66666(5   666666   666666   666666   666666 
487681)   468787   398688   287868   398868 


LESSON  XXVIII. 


(235)  (236) 

777777   777777 
387989   486788 


(237)      (238)      (239) 

777777   777777   777777 
298788   287888   297998 


(240)      (241) 

888888   888888 
189889   189899 


(242)      (243)      (244) 

888888   888888   888888 
188889   198889   189889 


(215)      (246)      (247)      (248)      (249) 

1000000  1000000  1000000  1000000  1000000 
999999   999999   999999   999999   999999 


8  from  9  leaves  1. 
8  n-on  10  leaves  2. 
8  from  11  leaves  3. 

10  +  8  —  ?  11+8: 

ll>_8=?    11—8: 

20  -f-8  =  ?  21  -f-8  : 
20  —  8=?  21—8: 
30  +  8  =  ?  31  +  8  . 
30-8=?  31-8: 
etc.  etc. 


SUBTRACTION. 


LESSON    XXIX. 

TABLE. 

8  from  12  leaves  4. 

8  from  13  leaves  5. 

8  from  14  leaves  6. 

Table  Exercise. 

12+8  =  ?  13 +8=?  14 +  8  =  ?  etc. 

12  —  8  =  ?  13  —  8  =  ?  14  —  8  =  ?  eb\ 

22  +  8  =  ?  23  +  8  =  ?  24  +  8  =  ?  etc. 

22  —  8  =  ?  23  —  8  =  ?  24  —  8  =  ?  etc. 

32  +  8  =  ?  33  +  8  =  ?  34  +  8  =  ?  etc. 

32  —  8  =  ?  33  —  8  =  ?  34  —  8  =  ?  etc. 
e  'c.       etc.       etc. 


8  ficm  15  leaves  7. 
8  from  16  leaves  8, 
8  from  17  leaves  9. 


BLACKBOARD    EXERCISES. 
(1) 

9     16     10     17     15     11     14     12     18     13 

8888888888 

(2) 
19     27     20     26     21     25     22     24     23     28 

8888888888 


29     37     30     36     31     35     34     33     38     32 

8888888888 


LESSON   XXX. 
MENTAL  EXERCISES. 

1.  There  were  18  bean-poles  in  a  row,  and  the  wind 
blew  down  8;  how  many  remained  standing? 

2.  15  boys  were  at  play;  a  shower  came  up,  and  only 
8  of  them  could  get  under  shelter;  how  many  got  wet? 

3.  Mary  had  16  roses  on  her  rose-bush;  Julia  plucked 
8  for  a  bouquet;  how  many  remained  on  the  bush? 


SUBTRACTION.  55 

4.  James  paid  19  cents  for  the  use  of  a  wheelbarrow, 
and  8  cents  for  the  use  of  a  spade ;  how  much  more  did 
he  pay  for  the  use  of  the  wheelbarrow  than  for  the  use 
of  the  spade. 

5.  There  are  18  girls  in  one  class  and  eight  in  another; 
how  many  more  girls  in  one  class  than  in  the  other? 

6.  James  put  20  cents  into  the  contribution  box,  John 
put  in  8;  how  many  more  did  James  put  in  than  John? 

7.  If  a  man  walked  23  miles  the  first  day,  and  8  miles 
the  second  day,  how  many  more  miles  did  he  walk  on  the 
first  day  than  on  the  second? 

8.  There  were  25  hats  in  a  row,  in  the  entry;  8  of 
them  are  taken  away;  how  many  remain? 

9.  Susan  paid  22  cents  for  some  muslin,  and  8  cents  for 
some  gingham ;  how  much  more  did  the  muslin  cost  than 
the  gingham? 

10.  Eight  boys  and  17  girls  were  picking  berries  in  a 
pasture;  how  many  more  girls  than  boys  were  there? 

LESSON    XXXI. 
WRITTEN  EXERCISES. 

Exercises  in  which  each  figure  in  the  Subtrahend  may  or  may  not 
be  larger  than  the  corresponding  figure  in  the  Minuend. 

(250)  (251)  (252)  (253)          (254) 

41878G  918746  918764  37842  671834 
126873  198714  168194  28468  103178 

(255)     (256)     (257)     (258)     (259) 

671837  418637  489683  916718  378724 
28713*  329672  341871  241803  160783 


56  SUBTRACTION, 

(2601  (261)  (262)  (263)  (264) 

418708  390641  983418  678371  918642 

387180  218901  371862  248713  167184 


LESSON   XXXII. 

(265)     (266)     (267)     (268)  (269) 

371864  918374  691371  8964137  418624 

214687  131989  113076  1178193  146193 


(270)     (271)     (272)     (273)     (274) 
341864  317834  671834  918641  378642 
143876  219873  142689  173868  119873 


(275)     (276)     (277)     (278)     (279) 
418637  418637  896834  918371  671837 
168901  389864  267891  267834  167990 


LESSON    XXXIII. 

(280)     (281)     (282)     (283)  (284) 

486413  418786  489134  600078  300000 

164184  219186  189193  112076  108819 


(285)     (286)     (287)     (288)     (289) 

600043  768374  9000134  ,687834  891670 
288811  237838  2999138  287788  191678 


(290)     (291)     (292)     (293)     (294) 

860783  418671  387891  678342  678913 
418787  141678  213874  328786  218673 


9  fi-oti  10  leaves  1. 
9  from  11  leaves  2. 
9  from  12  leaves  3. 


10  +  9  =  ?  11  -f-9  : 
10  —  9  =  ?  11  —  9  : 
20+9  =  ?  21  +  9  : 
20  —  9  =  ?  21  —  9  : 
30  +  9=?  31  +  9: 
30  —  9=?  31  —9  : 
etc.  etc. 


SUBTRACTION. 


IESSON  xxxiv. 


9  from  13  'eaves  4.     9  from  16  leaves  7. 

9  from  14  leaves  5.     9  from  17  leaves  8. 

9  from  15  leaves  6.     9  from  18  leaves  9. 

Table  Exercise. 

:?  12  +-  9  =?  13  +  9  =  ?  14+5  =  ?  etc. 
:?  12  —  9=?  13  —  9  =  ?  14-5  =  ?  etc. 
:?  22  +  9  =?  23  +  9  =  ?  24+  5=-?  etc. 
:?  22  —  9=?  23  —  9  =  ?  24  —  5  =  ?  etc. 
:?  32  +  9  =?  33  +  9  =  ?  84  +  5  =  ?  etc. 
:?  32  —  9=?  33  —  9  =  ?  84  —  5  =  ?  etc. 
etc.  etc.  etc. 


BLACKBOARD    EXERCISES. 
(1) 

9       5     10     18     12     11     H     13     14     16     17 
99999999999 


19     21     20     22     28     27     23     25     24     26 
9999999999 

(3) 

29     31     30     33     32     35     34     38     37     36 
9999999999 


LESSON   XXXV. 
MENTAL  EXERCISES. 

1.  If  John  lias  one  apple  and  gives  it  to  William,  how 
many  has  he  left? 

2.  If  Charles  has  0  oranges  and  his  older  brother  takes 
them  from  him,  how  many  will  he  have  left? 

3.  James  saw  15  birds  on  a  tree;  9  flew  away,  how 
many  remained? 


58 


SUBTRACTION. 


4.  Reuben  had  14  cherries,  he  ate  9;  how  many  had 
lie  left? 

5.  There  were  11  chairs  in  the  room;  9  were  taken 
away,  how  many  remained? 

6.  There  were  28  sheep  in  a  fold,  a  wolf  broke  in  and 
killed  9 ;  how  many  were  left  alive  ? 

7.  There  are  27  scholars  in  a  school;  9  of  them  are 
boys,  how  many  are  girls? 

8.  Montgomery  has  31  cents,  he  spends  9  cents  for 
pea-nut  candy ;  how  many  cents  has  he  left. 

9.  Alexander  ate  5  cents'  worth  of  the  candy;  how 
much  is  left  for  Montgomery? 

10.  Ada  has  19  pins  in  her  cushion;  Nettie  takes  out 
2  and  Nellie  7 ;  how  many  pins  remain  in  the  cushion  ? 

11.  Willie  bought  22  marbles,  but  in  the  first  game  he 
lost  9;  how  many  had  he  left? 

12.  Ella  is  16  years  old  and  Willie  is  only  4  years, 
how  much  older  is  Ella  than  Willie? 

1 3.  Ella  is  1 6  years  old  and  Julia  is  9,  how  much  older 
is  Ella  than  Julia? 

LESSON   XXXYL, 

WRITTEN  EXERCISES. 

(295)  (2-VJ  (2iT,)  (298) 

41878G434  91878C413  918718642  918718642 
48041783   21867183  418938648  318718648 


(299)        (30C)        (301)        (302) 

878641378  41878612  3967837864  418786243 
138964179  34188762   139180067  213786983 


SUBTRACTION.  59 

(303)                   (304)                   (305)  (306) 

41878G43  918768434  S71864153  918G70034 

20878699   30190132   41878642  31671832 


LESSON    XXXVII. 

(307)  (308)  (309)  (310) 

4000700  3000007  410010106  370130712 

64    40009  110101006  171031719 


(311)       (312)       (313)       (31-1) 

67083701  91876412.  4187643  9187G884 
24083710   3876814  1738878  11761023 


(315)       (316)       (317)      (318) 

40000006  40000000  2000000  6000000 
30000009  36666667   188889  5999999 


LESSON    XXXVIII. 
(319)  (320)  (321)  (322) 

60000000  910101010  4040404  801080180 

11030103  801010101  3014401  710181081 


(323)       (324)       (325)       (326) 

41803012  41867083  64187839  418786412 
13814236  31210789  13117814     211030 


(327)       (328)       (320)       (330) 

41860003  20300000  6700000  406010416 
17001   1000009    10109   14661210 


60  SUBTRACTION. 

331.  A  man  sold  347  pounds  of  rice  to  one  man  and 
427  pounds  to  another;  how  many  pounds  did  he  sell  in 
all? 

332.  A, merchant  sold  430  yards  of  calico  to  one  man 
and  2£0  yards  to  another ;  how   much   did  he   sell  to 
both? 

333.  A  farmer  bought  36  sheep  for  137  dollars  at 
one  time,  and  47  sheep  for  220  dollars  at  another  time ; 
how  much  did  the  sheep  cost  him  ? 

334.  A  man  bought  367  yards  of  calico  for  which  he 
paid  37  dollars,  he  sold  it  so  as  to  gain  23  dollars  j  how 
much  did  he  sell  it  for  ? 

335.  A  boy  bought  38   marbles,  but  afterward  lost 
17  ;  how  many  marbles  had  he  left  ? 

336.  A  boy  gave  a  dollar  bill  to  pay  for  a  slate  that 
cost  34  cents;  how  much  change  should  he  receive  back  ? 

337.  A  boy   gave  a  dollar  bill  to  pay  for  2  books 
which  cost  98  cents ;  how  much  change  should  he  receive  ? 

338.  A  little  girl  had  a  three-dollar  bill,  she  wished 
to  buy  a  doll  which  cost  90  cents ;  how  much  change 
should  she  receive  ? 

339.  A  little  girl  had  a  five- dollar  bill,  she  bought  a 
book  for  99  cents ;  how  much  change  should  she  receive  ? 

340.  A  little  boy  had  a  fifty-cent  piece,  he  bought  a 
slate,   pencil   and    arithmetic    for  43    cents :  the    shop- 
keeper gave  him  5  cents  change ;  what  should  he  have 
received  ? 

34-1.  Samuel  bought  a  melon  for  94  cents,  he  gave  a 
dollar  bill  and  received  15  cents  change;  how  much 
Should  he  have  received  ? 


SUBTRACTION.  61 

342.  Arthur  and  James  paid  for  a  bushel  of   nuts 
which  cost  437  cents,  Arthur  paid  240  cents  and  James 
was  to  pay  the  remainder ;  he  gave  a  two-dollar  bill ; 
should  he  receive  any  change  ? 

343.  A   man  bought  a  house  for   834  dollars ;  how    , 
much  will  he  have  left  of  a  thousand-dollar  bill  ? 

344.  A  man  bought  a  horse   for  195  dollars;    how 
much  change  should  he  receive  from  two  hundred-dollar 
bills  ? 

345.  A  boy  had  113  marbles,  he  bought  25  more; 
how  many  had  he  then  ?     He  then  gave  away  1 1 ;  how 
many  had  he  left?     How  many  more  must  he  get    to 
make  the  number  200  ? 

346.  A  grocer  paid  370  cents  for  a  box  of  raisins  and 
480  cents  for  some  oranges  ;  how  much  more  did  he  give 
for  the  oranges  than  the  raisins  ? 

347.  A  farmer  had  340  pounds  of  cheese,  he  sold  260 
pounds  ;  how  much  remained  ? 

348.  A  man  is  320   miles  from   home  after*  he  had 
travelled  46  miles  ;   how  far  is  he  from  home  ? 

349.  A  little  boy  ran  44  rods  up  the  road  and  then 
ran  back;  how  far  did  he  run  in  all? 

350.  Two  little  boys  started  to  run  a  race,  one  ran  53 
rods  the  other  29  rods ;  how  far  were  they  apart  ? 

351.  A  boy  shot  an  arrow  up  the  road  173  feet,  and 
another  down  the  road  211   feet;  how  far  were  the  ar- 
rows apart  ? 

352.  He  asked  a  little  boy  to  bring  the  arrows  to 
him  ;  how  far  must  he  walk  to  get  them  ? 


SECTION  IV. 

LESSON    I. 

If  there  are  10  windows  on  one  side  of  a  car,  how 
many  windows  on  both  sides  of  the  car  ? 

FORMULA. — If  there  are  10  windows  on  one  side  of  the  car,  on  both 
sides  there  are  2  times  10  windows,  which  is  20  windows;  therefore 
there  are  20  windows  in  the  car. 

1.  If  1  lead  pencil  costs  3  cents  what  will  2  lead  pen- 
cils cost  ? 

FORMULA.— If  Head  pencil  costs  3  cents,  2  lead  pencils  will  cost  2 
tin.es  3  ents,  which  are  6  cents. 


MULTIPLICATION.          •  63 

The  -efore,  if  1  lead  pencil  costs  3  cents,  2  lead  pencils  will  cost 
5  cents. 

2.  If  1  hoop  costs  6  cents  how  much  will  2  hoops  cost 
at  the  same  rate  ? 

3.  There  are  5  apples  on  one  branch,  how  many  apples 
on  two  such  branches? 

4.  James  was  fishing  two  hours;  he  caught  7  fishes 
each  hour;  how  many  fishes  did  he  catch? 

5.  If  one  cocoa-nut  is  worth  8  cents,  how  much  are 
two  cocoa-nuts  worth? 

6.  What  cost   2   quarts   of  chestnuts  at   12   cents   a 
quart?  at  9  cents?  at  11  cents? 

7.  At  10  cents  a  gallon,  what  cost  two  gallons  of  vine- 
gar? 

8.  If  butter  is  12  cents  a  pound,  what  will  2  pounds 
cost? 

9.  In  1  dime  there  are  10  cents ;  how  many  cents  in  2 
dimes? 

10.  In  1  quart  there  are  2  pints ;  how  many  pints  in  7 
quarts? 

11.  There  are  2  halves  in  one  unit;  how  many  halves 
in  6  units? 

12.  If  one  book  costs  1  cent,  what  will  two  books  cost? 

13.  If  one  apple  costs  two  cents,  what  will  9  apples 
cost? 

14.  What  cost  2  quarts  of  walnuts  at  8  cents  a  quart? 
at  7  cents  ?  at  4  cents? 

15.  If  \  inkstard  costs  6  cents  what  will  2  inkstands 
cost? 


64  .        MULTIPLICATION. 

LESSON  III. 

WRITTEN"  EXERCISES,* 

In  which  the  product  of  each  figure  does  not  exceed  nine. 
(1)  (2)  (3)  (4)  (5) 

130243  240143  324123  34121043  21434213 
222        2        2 

__________  •».——.  _______^_  * 

(6)       CO        (8)        (9)       (10) 

340432  4412304  3241230  4130423  4130243 
22222 


(11)       (12)       (13)        (14)         (16) 

804034   3401043  34234204  34142304   30412343 
2222        2 


LESSON  IV. 

(16)      (17)   .     (18)       (19)       (20) 

403402  3042043  4203042  3042041  3042304 
22222 


(21)        (22)       (23)        (24)        (25) 

4304014   3042043   4304123   4230423   412S0413 
22222 


(26)       (27)      (28)      (29)      (30) 
3040204  4302432  423042  340243  3204302 
22222 


*  To  THE  TEACHER  — The  teacher  should  tak«  occasion  to  explain  the  method 
»f  multiplication  when  the  product  of  each  figure  does  not  exceed  nine. 


MULTIPLICATION. 


LESSON   V. 
TABLE. 


Once    0  »3    0. 

0  times  2  are     0. 

0  times  3  a1  e     0. 

Once     1  is     1. 

1  times  2  are     2. 

1  times  3  are     3. 

Once     2  is     2. 

2  times  2  are     4. 

2  times  3  are     6. 

Once     3  is     3. 

3  times  2  are     6. 

3  times  3  are     9. 

Once    4  is    4, 

4  times  2  are     8. 

4  times  3  are  12. 

Once     5  is     5- 

5  times  2  are  10. 

5  times  3  are  15. 

Once     6  is     6, 

6  times  2  are  12. 

6  times  3  are  18. 

Once     7  is     7. 

7  times  2  are  14. 

7  times  3  are  21. 

Once     8  is     8. 

8  times  2  are  16, 

8  times  3  are  24 

Once     9  is     9. 

9  times  2  are  18. 

9  times  3  are  27. 

Once  10  is  10. 

10  times  2  are  20. 

10  times  3  are  30. 

Once  11  is  11. 

11  times  2  are  22. 

11  times  3  are  33. 

Once  12  is  12. 

12  times  2  are  24. 

12  times  3  are  36. 

BLACKBOARD    EXERCISES. 
(1) 

132074658  10  11  9  12 
333333333   3   33   3 


(2) 

33       333       33       333333 
01     12     23     11     4     10     59687 


LESSON    VI. 
MENTAL  EXERCISES. 

1.  If  one  sheep  cost  2  dollars,  what  will  3  sheep  costf 

SOLUTION. — The  solution  is  the  same  as  in  the  preceding  exer- 
cises. 

2.  A  butcher  paid  2  dollars  a  head  for  sheep,  what 
will  7  sheep  cost  at  that  rate? 

3.  What  will  3  hats  cost  at  8  dollars  a  piece? 

4.  At  8  dollars  a  week  how  much  will  a  man  earn  in 
*hree  weeks? 


66  MULTIPLICATION. 

4.  In  a  half-dime  there  are  5  cents;  how  many  cents 
in  3  half-dimes? 

5.  Twelve  single  things  make  a  dozen;  how  many 
single  things  make  3  dozen? 

6.  There  are  ten  cents  in  one  dime;  how  many  cents 
are  there  in  3  dimes? 

7.  In  one  dram,  Apothecaries'  Weight,  there  are   3 
scruples;  how  many  scruples  in  9  drams  of  the  same 
weight? 

8.  There  are  7  days  in  a  week;  how  many  days  in 
three  weeks? 

9.  If  a  boy  works  5  hours  in  a  day,  how  many  hours 
does  he  work  in  3  days? 

10.  There  are  9  square  feet  in  a  square  yard;  how 
many  square  feet  in  3  square  yards? 

11.  There  are  11  hop-poles  in  a  row;  how  many  hop- 
poles  in  three  such  rows? 

12.  In  a  dozen  there  are  12  units,  how  many  units  in 
3  dozen? 

13.  What  will  9  oranges  cost  at  3  cents  each? 

14.  What  will  4  pairs  of  boots  cost  at  3  dollars  a  pair? 

15.  What  will  7  yards  of  tape  cost  at  3  cents  a  yard? 

16.  What  will  9  pairs  of  cotton  gloves  cost  at  3  shil- 
lings a  pair? 

17.  What  will  3  books  cost  at  9  shillings  apiece? 

18.  In  one  unit  there  are  3  thirds;  how  many  thirds 
in  8  units  ? 

19.  In  one  orange  there  are  7  sevenths ;  how  many 
sevenths  in  3  oranges  ? 

20.  In  one  unit  there  are   12   twelfths;  how  many 
-  are  there  in  3  units  ? 


MULTIPLICATION. 


67 


LESSON    VII. 

WRITTEN  EXERCISES,* 

la  which  the  product  of  each  figure  equals  or  exceeds  nine  but  ia 


less  than  twenty. 


131)       (32)       (33) 
4563464  3456356  3435634 
333 


(34)      (35) 
4343654  345346 
3      3 


(36)       (37)       (38)      (39)       (40) 
4364364  3464354  4356434  433465  43456434 
3333        3 


(41)       (42)       (43)       (44)       (45) 

3454364  3446454  3434464  3430345  4343434 
3       3       3       33 


LESSON  VIII. 

(46)       (47)       (48)        (49)       (50) 
4343445  6434645  3464354  34435456  3434456 
33333 


(51)       (52)       (53)       (54)       (55) 

3456454  3454645  4543456  6534356  3545464 
33333 


(56)       (57)        (58)       (59)        (60) 

4345464  43454345  45345464  54345434  54345345 
33333 


*  NOTE  — The  teacher  should  take  occasion  to  explain  the  method  of  carrying 
when  the  product  of  each  figure  exceeds  nine. 


68  MULTIPLICATION. 

LESSON    IX. 
TABLE. 

1  time    <1  is        4.  I  5  times  4  are  20.  I     9  tiroes  4  are  36. 

2  times  4  are      8.  I  6  times  4  are  24.  |  10  times  4  are  40. 

3  times  4  are  12.  I  7  times  4  are  28.  I  11  times  4  are  44. 

4  times  4  are  16.  |  8  times  4  are  32.  |  12  times  4  are  48. 

Table  Exercise. 

10 +  4  =  ?  11  4-4  =  ?  12  4-4=?  ]3  +  4=?  14  +  4  =  ?  e.c. 
10  —  4  =  ?  11  —  4  =  ?  12  —  4  =  ?  13  —  4  =  ?  14  —  4  =  ?  etc. 
10  x  4  =  ?  11  x  4  =  ?  12  x  4  =  ?  13  x  4  =  ?  14  x  4  =  ?  etc. 
20  4-  4  =  ?  21  4-  4  =  ?  224-4=?  23  -h  4  =  ?  24  4~  4  =  ?  efc. 
20  -  4  =  ?  21  —  4  =  ?  22  —  4  =  ?  23  —  4  =  ?  24  —  4  =  ?  etc. 
20x4  =  ?21x4  =  ?22x4=?  23x4  =  ?24x4  =  ?  efc. 
304-4  =  ?  31+4  =  ?  32+4  =  ?  33  +  4=?  344-4  =  ?  etc. 
etc.  etc.  e1c.  etc.  etc. 

BLACKBOARD    EXERCISES. 
(1) 

0192  11  12  38  10  4756 
4444   4   444   44444 


44444   444444   4   4 
10243  12  57698  11  10 


LESSON   X. 
MENTAL  EXERCISES. 

1.  In  one  yard  there  are  3  feet;  how  many  feet  are 
there  in  four  yards? 

2.  There  are  4  gills  in  one  pint;  how  many  gills  in  7 
pints  ? 

3.  There  are  5  quires  in  a  quarter  of  a  ream  of  pa- 
per; how  many  quires  in  four  quarters  of  a  ream? 

4.  If  there  are  7  days  in  one  week,  how  many  days  in 
four  weeks? 


MULTIPLICATION.  69 

5.  If  a  cannon  ball  weighs  4  pounds,  how  much  will  8 
balls  of  the  same  size  weigh? 

6.  There  are  eight  quarts  in  a  peck;  how  many  quarts 
in  11  pecks? 

7.  There  are  4  hop-poles,  each  pole  is  12  feet  long, 
what  is  the  united  length  of  the  four  poles? 

8.  There    are   4   quarters  w  one  apple;   how  many 
quarters  in  6  apples? 

9.  There  are    7    sevenths   in   one   apple,  how  many 
sevenths  in  4  apples? 

10  There  are  9  ninths  in  one  unit;  how  many  ninths 
in  4  units? 

11.  What  will  4  hats  cost  at  12  shillings  apiece? 

12.  What  will  4  kites  cost  at  a  cent  apiece? 

13.  There  are  8  eighths  in  one  unit?  how  many  eighths 
in  4  units  ? 

14.  If  1  slate  is  worth  11  cents,  how  much  are  4  slates 
worth  ? 

15.  If  4  weeks  make  a  month,  how  many  weeks  in  8 
months  ? 

16.  If  1  pair  of  boots  costs  5  dollars  what  will  4  pairs 
cost? 

17.  If  1  cap  costs  10  shillings,  what  will  4  caps  cost 
at  the  same  price  ? 

18.  If  a  man  can  eat  12  ounces  of  bread  in  one  day, 
how  much  can  4  men  eat  in  the  same  time  ? 

19.  If  6  men  can  drink  4  gallons  of  beer  in  a  week, 
how  many  gallons  can  they  drink  in  9  weeks? 

20.  If  one  man  can  drink  9  gallons  of  cider  in  2  weeks, 
how  many  gallons  can  4  men  drink  in  the  same  time  ? 


70 


MULTIPLICATION. 
LESSON    XI. 


WRITTEN  EXERCISES, 

In  which  the  product  of  each  figure  may  or  may  not  exceed  nine 
(61)  (62)  (63)  (64)  (65) 

134046  41341234  4134542  6783741  8371246 
4        4-444 

(66)       (67)       "(68)       (69)       (70) 

3404134  634243  4137404  1678343  6783437 
44444 


(71)      (72)       (73)     (74)       (75) 
437489  6789013  978649  345987  4139764 
44444 


LESSON    XII. 

76.  Multiply  3846783467  by  2,  by  3,  by  4 

77.  Multiply  8706346782  by  2,  by  3,  by  4r 

78.  Multiply  4167834086  by  2,  by  3,  by  4- 

79.  What  costs  16  pounds  of  rice  at  5  cents  a  pound  ? 

80.  What  costs  320  apples  at  4  cents  each  ? 

81.  What  costs  3  pounds  of  tea  at  138  cents  per  pound '? 

82.  How  many  feet  have  130  horses  ? 

83.  How  many  corners  have  437  slates  ? 

84.  How  many  toes  have  two  boys  ? 

85.  How  many  fingers  have  three  girls? 

86.  How  many  feet  have  four  flies? 

87.  How  many  wheels  have  320  wagons  ? 

88.  How  many  quarters  in  46  apples? 

89    How  many  corners  have  four  square  boxes  ? 
9D.   How  many  walls  in  20  square  rooms  ? 


1  time   5 
2  times  5 
3  times  5 
4  times  5 

\ 

is       5. 
are  10. 
are  15. 
are  20. 

MU  LTIPLIC  ATION. 

LESSON    XIII. 
TABLE. 

5  times  5  are  25. 
6  times  5  are  30. 
17  times  5  are  35. 
8  times  5  are  40. 
Table  Exercise. 

9  times  5  are 
10  times  5  are 
11  times  5  are 
12  times  5  are 

45. 
50. 
55. 
60. 

10  +  5  = 

?  11 

+  5,   12  +  5 

; 

13  +  5 

;  14  +  5 

;  etc. 

10- 

5  = 

?  ll 

— 

5;   12 

—  5 

;   13-5 

;  14  —  5 

;  etc. 

10  x 

5  = 

?  11 

x 

5;   12 

x  5 

i 

13  x 

5 

;  14  x  5 

;  etc. 

20  + 

5  =^ 

?  21 

+ 

5;   22 

+  5 

» 

23  +  5 

;  24  +  5 

;  etc. 

20  — 

5  = 

?  21 

5;   22 

-  5 

;  23  —  5 

;  24—  5 

;  etc. 

20  x 

5  = 

?  21 

x 

5;   22 

x  5 

i 

23  x 

5 

;  24  x  5 

;  etc. 

30  -f 

5  = 

?  31 

+  5;  32  +  5 

> 

33  +  5 

;  34  +  5 

;  etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

BLACKBOARD   EXERCISES. 

(1) 

1     9 

10 

2 

8 

6 

7 

3 

11 

5     12 

4 

0 

5     5 

5 

5 

5 

5 

5 

5 

5 

5       5 

5 

5 

(2) 

5     5 

5 

5 

5 

555 

5 

5       5 

5 

5 

1     2 

0 

3 

5 

476 

12 

8     11 

10 

9 

71 


LESSON   XIV. 
MENTAL  EXERCISES. 

1.  Charlss  brought  two  chairs  into  the  room  each  time 
he  came  in;  how  many  chairs  did  he  bring  in,  in  coming 
five  times? 

2.  There  are  5  hills  of  corn  in  one  row,  how  many  hills 
in  7  rows? 

3.  In  one  unit  there  are  5  fifths,  how  many  fifths  in  9 
units? 


rZ  MULTIPLICATION. 

•-    4.  There  are  10  tenths  in  one  apple,  how  many  tenths 
in  5  apples  ? 

5.  If  one  pound  .>f  sugar  cost  5  cents,  how  many  cents 
will  12  pounds  cost? 

6.  One  piece  of  tape  costs  11  cents;  how  much  will  5 
pieces  cost? 

7.  There  are  ten  cents  in  one  dime;  how  many  cents 
in  five  dimes? 

8.  If  a  boy  performs  12  examples  each  day,  how  many 
will  he  perform  in  5  days  ? 

9.  There  are  6  books  in  a  row;  how  many  books  in 
5  such  rows? 

10.  If  1  top  costs  two  cents,  how  much  will  5  tops 
cost? 

11.  One  kite  costs  4  cents;  how  much  will  5  kites  cost 
at  the  same  rate? 

12.  I  have  five  sticks,  each  3  feet  long;  what  is  the 
united  length  of  the  sticks? 

LESSON    XV. 
-     WRITTEN  EXERCISES. 

91.  Multiply  378641783  by  2,  by  3,  by  4,  by  5. 

92.  Multiply  478600324  by  2,  by  3,  by  4,  by  5. 

93.  Multiply  378641834  by  2,  by  3,  by  4,  by  5. 

94.  Multiply  468371834  by  2,  by  3,  by  4,  by  5. 

95.  Multiply  37186004  by  2,  by  3,  by  4,  by  5. 

96.  Multiply  378642014  by  2,  by  3,  by  4,  by  5. 

97.  Multiply  42786423  by  2,  by  3,  by  4,  by  5. 

98.  Multiply  37862404  by  2,  by  3,  by  4,  by  6. 
89.  Multiply  33420423  by  2,  by  3,  by  4,  by  5. 


MULTIPLICATION.  73 

LESSON   XVI. 

100.  What  will  4070  lemons  cost  at  2  cents  each  ? 
At  3  cents  each  ?     At  4  cents  each  ?     At  5  cents  each  ? 

101.  What  will  87086  oranges  cost  at  2  cents  each? 
At  3  cents  each  ?     At  4  cents  each  ?     At  5  cents  each  ? 

102.  A  man  paid  387  dollars  for  a  house;  how  much 
should  he  give  for  2  such  houses  ?     For  3  such  houses  ? 
For  1  such  houses  ?     For  5  such  houses  ? 

103.  What  must  I  give  for  487  apples  at  2  cents  each  ? 
At  3  cents  each  ?  At  4  cents  each  ?  At  5  cents  each? 

104.  How  many  halves  in  3437  apples?     How  many 
thirds  ?     How  many  fourths  ?     How  many  fifths  ? 

105.  A  man   bought  3742  apples  at  2    cents   each, 
260653  oranges  at  4  cents  each,  4989  peaches  at  3  cents 
each,  3742  lemons  at  5  cents  each;  what  did  each  cost? 

106.  Write  341372  twice  and  add  it;  write  it  three 
times  and  add  it ;   write  it  four  times ;  five  times. 

107.  A  man   bought  at  oue  time  6608  pounds  of  cot- 
ton, at  another  398   pounds ;  how  many  pounds  had  he 
then?     He  afterward  sold  5871  pounds  ;  how  much  had 
he  left  ?     He  then  sold  ^97  pounds  of  the  remainder; 
how  much  did  he  still  have  ?     He  finally  bought  1588 
pounds;  how  much  did  he  then  have? 

108.  Three   hundred  and   twenty-four  dollars  is  one- 
half  of  what  number  of  dollars  ?  324  dollars  is  one  third 
of  what  number  of  dollars  ?  324  dollars  is  one-fourth  of 
what  number  of  dollars  ?  324234  dollars  is  one-fifth  of 
what  number  of  dollars  ? 

109.  What  will  3043  pair  of  boots  cost  at  2  dollars  a 
pair  ?     At  3  dollars  ?     At  4  dollars  ?     At  5  dollars  ? 


74 


MULTIPLICATION. 


LESSON  XVII. 

TABLE. 

1  time    6  is       6. 

5  times  6  are  30. 

9  times  6  are  54, 

2  times  6  are  12. 

6  times  6  are  36. 

10  times  6  are  60. 

3  times  6  are  18. 

7  times  6  are  42. 

11  times  6  are  66. 

4  times  6  are  24. 

8  times  6  are  48. 

12  times  6  are  72. 

Table  Exercise. 

10  +  6;   11  4-6 

12  +  6;    13  +  6;  14+6;  15  +  6;  etc. 

10  —  6;  11  —  6 

12  —  6;    13  —  6 

14  —  6;  15  —  6;  etc. 

10  x  6;  11  x  6 

12  x  6;   13  x  6 

14  x  6;  15  x  6;  etc. 

20  +  6;  21+6 

22  +  6;    23+6 

24  +  6  ;  25  +  6  ;  etc. 

20  —  6;  21  —  6 

22  —  6;   23  —  6 

24  —  6;  25  —  6;  etc, 

20  x  6;  21  x  6 

22  x  6  ;   23  x  6 

24  x  6  ;  25  x  6  ;  etc. 

30  +  6;  31+6 

32  +  6;   33  +  6 

34  +  6  ;  35  +  6  ;  etc. 

e'c.          etc            etc.           etc. 

ec.           etc. 

BLACKBOARD    EXERCISES. 


1204 

6666 


(l) 

12  5  3  9  8  6  10  7  11 
666666   66   6 


66666 
10234 


(2) 

6   66   66666 
11  10  9  12  8765 


LESSON   XVIII. 

1.  If  you  give  one  cent  for  a,  pencil,  how  many  cents 
must  you  give  for  6  pencils  at  the  same  rate? 

2.  If  one  lemon  costs  2  cents,  what  will  six  lemons 
cost? 

3.  If  one  orange  costs  3  cents,  what  will  6  oranges 
cost? 

4.  What  will  7  melons  cost  at  6  cents  apiece? 

5.  What  will  9  skeins  of  silk  cost  at  6  cents  apiece? 


MULTIPLICATION.  75 

6.  What  will  11  boxes  of  lemons  cost  at  6  dimes  0 
box? 

7.  At  8  shillings  a  bushel,  what  cost  six  bushels  of 
sweet  potatoes? 

8.  At  9  cents  a  pound,  what  cost  6  pounds  of  cheese? 

9.  If  I  can  earn  10  dollars  in  one  month,  how  much 
can  I  earn  in  6  months? 

10.  John  spent  7  dollars  in  one  month;  how  much  at 
that  rate,  will  he  spend  in  6  months? 

11.  A  freight  train  can. run  11  miles  in  an  hour;  how 
many  miles  at  that  rate,  can  it  run  in  6  hours? 

12.  If  a  horse  travels  12  miles  in  a  day,  how  far  at  that 
rate  will  he  travel  in  6  days? 

13.  At  9  cents  a  pound,  how  much  will  6  pounds  of 
s*ugar  cost? 

14.  At  8  cents  a  pound,  how  much  will  6  pounds  of 
rice  cost? 

15.  I  purchased  6  writing-books  at  10  cents  each,  what 
was  the  cost? 

16.  How  much  will  10  inkstands  cost  at  6  cents  each? 

17.  In  one  unit  there  are  6  sixths;  how  many  sixths 
in  11  units? 

18.  In  one  unit  there  are  10  tenths;  how  many  tenths 
in  6  units? 

19.  In  one  apple  there   are  4  quarters,-  how  many 
quarters  in  6  apples? 

20.  If  the  interest  on  one  dollar  for  one  year  is  8  cents, 
What  will  be  the  interest  on  6  dollars  for  the  same  time  ? 


7G 


MULTIPLICATION. 


LESSON    XIX. 
WRITTEN  EXERCISES. 

(110)  (111)  (112)  (113)  (114) 

3741064      34071064     3718643     41890701      4196804 
66666 


(115)  (116)  (117)  (118)  (119) 

37604134      6786804     3740134     6896083      41968341 
6666  6 


(120)  (121)  (122)  (123}  (124) 

3718642  4186742  3786413  4908370  37186412 
66666 


LESSON    XX. 

125.  Multiply  37418643  by  3,  by  4,  by  5,  by  6. 

126.  Multiply  4683413  by  3,  by  4,  by  5,  by  6. , 

127.  Multiply  3424160  by  3,  by  4,  by  5.  by  6. 

128.  Multiply  4680309  by  3,  by  4,  by  5,  by  6. 

129.  Multiply  32016092  by  3,  by  4,  by  5,  by  6. 

130.  Multiply  20680437  by  3,  by  4,  by  5,  by  6. 

131.  Multiply  30641872  by  3,  by  4,  by  5,  by  6. 

132.  Multiply  34670843  by  3,  by  4,  by  5,  by  6. 

133.  Multiply  48678342  by  3,  by  4,  by  5,  by  6. 

134.  Multiply  37864372  by  3,  by  4,  by  5,  by  6. 

135.  Multiply  39786042  by  3,  by  4,  by  5,  by  6. 

136.  Multiply  4234671  by  3,  by  4,  by  5,  by  6. 

137.  Multiply  3246721  by  3,  by  4,  by  5,  by  6. 

138.  Multiply  4234261  by  3,  by  4,  by  6,  by  5. 

139.  Multiply  3241632  by  3,  by  4,  by  6,  by  5. 


MULTIPLICATION. 


LESSON    XXI. 


77 


TABLE. 

1  time   7 
2  times  7 

is 

are 

7. 

14. 

5  times 
Q  times 

7  are 
7  are 

35. 

42. 

9  times  7  are  63. 
10  times  7  are  70. 

3  times  7 

are 

21. 

7  tim  s 

7  are 

49. 

11 

times  7  are 

77. 

4  times  7 

are 

28. 

8  times 

7  are 

56. 

12  times  7  are 

84. 

Ta6£e  Exercise. 

10  +  7; 

11 

+  7; 

12  +  7; 

13  +  7  :  14+7 

'i 

15  +  7 

efc. 

10  —  7; 

11 

—  7; 

12  —  7; 

13  — 

7;  14  —  7; 

15  —  7 

; 

efc. 

10x7; 

11 

x  7; 

12  x  7; 

13  x 

7;  14  x  7; 

15  x  7 

5 

efc. 

20  +  7  ; 

21 

+  *; 

22  +  7  ; 

23  + 

7  ;  24  +  7 

i 

25  +  7 

? 

etc. 

20  —  7; 

21 

—  V; 

22  —  7; 

23  — 

7;  24  —  7 

'•> 

25  —  7 

; 

etc. 

20  x  7; 

21 

x  7; 

22  x  7; 

23  x 

7  ;  24  x  7  ; 

25  x  7 

; 

ftc. 

30  +  7; 

31 

+  7;  32  +  7; 

33  + 

7;  34  +  7 

> 

35  +  7 

» 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

etc. 

BLACKBOARD    EXERCISES. 
(1) 

12  01768295  10  3  11  4 

777777777   77   77 


(2) 

77777777 
04132675 


111       1       1 
12     98     11     10 


LESSON    XXII. 
MENTAL  EXERCISES. 

1.  Since  there  are  2  pints  in  one  quart,  how  many 
pints  in  7  quarts? 

2.  In  one  unit  there  are  9  ninths,  how  many  ninths  in 
7  units? 

3.  What  will  7  pairs  of  shoes  cost  at  2  dollars  a  pair? 

4.  What  will  9  barrels  of  flour  cost  at  7  dollars  a 
barrel  ? 


78  MULTIPLICATION. 

5.  What  will  11  yards  of  broadcloth  cost  at  7  dollars 
a  yard? 

6.  What  will  12  books  cost  at  7  shillings  a  volume? 

7.  Since  there  are  3  feet  in  one  yard,  how  many  feet 
in  7  yards? 

8.  There  are  4  gills  in  one  pint;  how  many  gills  in  7 
pints, 

9.  The  interest  on  one  dollar  for  one  year  in  the  state 
of  New  York  is  7  cents;  what  is  the  interest  on  12  dol- 
lars for  the  same  time  in  the  same  state? 

10.  The  interest  on  one  dollar  for  one  year  in  the  state 
of  New  Jersey  is  6  cents;  what  is  the  interest  on  7  dol- 
lars in  the  same  state  for  the  same  time? 

11.  There  are  7  days  in  one  week;  how  many  days  in 
9  weeks? 

12.  There  are  9  square  feet  in  one  square  yard;  how 
many  square  feet  in  7  square  yards? 

13.  James  is  8  years  old;  how  old  will  he  be  when  he 
is  7  times  as  old  as  he  now  is? 

14.  There  are  12  inches  in  one  foot;  how  many  inches 
in  7  feet? 

15.  What  cost  9  baskets  of  peaches  at  7  shillings  a 
basket? 

16.  A  boy  earned  7  shillings  in  one  week;  how  much 
at  that  rate  can  he  earn  in  9  weeks? 

17.  George  learned  7  pages  of  Greek  in  one  week;  at 
that  rate  how  much  will  he  learn  in  11  weeks? 

18.  Montgomery  required  Heberton  to  perform  12  ex- 
amples in  Algebra  at  one  lesson ;  at  that  rate  how  many 
examples  will  he  perform  in  7  weeks? 


MULTIPLICATION.  7J 

LESSON    XXIII. 
WRITTEN  EXERCISES. 
HO.  Multiply  3741867  by  4,  by  5,  by  6,  by  7. 

141.  Multiply  4786344  by  4,  by  5,  by  6,  by  7. 

142.  Multiply  4978672  by  4,  by  5,  by  6,  by  7. 
143..  Multiply  3741863  by  4,  by  5,  by  6,  by  7. 

144.  Multiply  4186742  by  4,  by  5,  by  6,  by  7. 

145.  Multiply  3968413  by  4,  by  5,  by  6,  fcy  7. 

146.  Multiply  9786421  by  4,  by  5,  by  6,  by  7. 

147.  Multiply  4871832  by  4,  by  5,  by  6,  by  7. 

148.  Multiply  467834  by  4,  by  5,  by  6,  by  7. 

149.  Multiply  1014702  by  4,  by  5,  by  6,  by  7. 

150.  Multiply  4345674  by  4,  by  5,  by  6,  by  7. 

151.  Multiply  3490416  by  4,  by  5,  by  6,  by  7. 

152.  Multiply  3708043  by  4,  by  5,  by  6,  by  7. 

LESSON   XXIV. 

153.  Multiply  9680724  by  4,  by  5,  by  6,  by  7. 

154.  Multiply  3968072  by  4,  by  5,  by  6,  by  7. 

155.  Multiply  4196718  by  4,  by  5,  by  6,  by  7. 

156.  Multiply  3419672  by  4,  by  5,  by  6,  by  7. 

157.  Multiply  89180034  by  4,  by  5,  by  6,  by  7. 

158.  Multiply  60789019  by  4,  by  5,  by  6,  by  7. 

159.  Multiply  1670834  by  4,  by  5,  by  6,  by  7. 

160.  Multiply  1307604  by  4,  by  5,  by  6,  by  7. 

161.  Multiply  4070683  by  4,  by  5,  by  6,  by  7. 

162.  Multiply  4030412  by  4,  by  5,  by  6,  by  7. 

163.  Multiply  3070412  by  4,  by  5,  by  6,  by  7. 

164.  Multiply  4030712  by  4,  by  5,  by  6,  by  7. 


80 


MULTIPLICATION. 


LESSON    XXV. 


TABLE. 

1  time    8  ia       8. 

5  times  8  are  40. 

9  times  8  are  72. 

2  times  8  are  16. 

6  times  8  are  48. 

10  times  8  are  80. 

3  times  8  are  24, 

7  tim  s  8  are  56. 

11  times  8  are  88. 

4  times  8  are  32. 

8  times  8  are  64. 

12  times  8  are  96. 

Table  Exercise. 

10  +  8 

11+8; 

12  +  8 

13  +  8;  14+8;  15  +  8 

etc. 

10  —  8 

11—8; 

12  —  8 

13  —  8;  14  —  8;   15  —  8 

etc. 

10  x  8 

11  x  8; 

12  x  8 

13  x  8;   14  x  8;   15  x  8 

etc. 

20  +  8 

21  +  8; 

22  +  8 

23  +  8;  24  +  8;  25  +  8 

etc. 

20  —  8 

21—8; 

22  —  8 

23  —  8;  24  —  8;  25  —  8 

etc. 

20  x  8 

21  x  8; 

22  x  8 

23  x  8  ;  24  x  8  ;   25  x  8 

(tc. 

30  +  8 

31  +  8; 

32  +  8 

33  +  8;  34  +  8;  35  +  8 

etc. 

etc.          etc. 

etc.           etc. 

etc.           etc. 

BLACKBOARD   EXERCISES. 


(1) 

105  6243  12  7 

8888888   88 


11 


10  9  8 

888 


(2) 

888   88   88   888888 
120  12  3  11  9  10  86754 


LESSON   XXVI. 
MENTAL  EXERCISES. 

1.  There  are  4  pecks  in  one  bushel;  how  many  pecks 
in  8  bushels? 

2.  What  will  8  books  cost,  if  one  book  cost  12  cents? 

3.  How  many  days  in  8  weeks?  in  7  weeks? 

4.  If  one  orange  costs  4  cents,  what  will  8  oranges  cost 
at  the  same  rate? 


MULTIPLICATION-  81 

5.  Peter  buys  8  lemons  at  8  cents  each  ;  what  do  they 


6.  Charles  bought  8  tops  at  4  cents  each;  what  did 
they  cost? 

7.  Henry  bought  11  pencils  at  8  cents  each;  what  did 
he  give  for  them? 

8.  Thomas  purchased  9  primers  at  8  cents  each  ;  what 
did  he  give  for  them? 

9.  Samuel  purchased  8  inkstands  at  12  cents  each; 
what  did  he  give  for  them? 

10.  In  one  unit  there  are  8  eighths;  how  many  eighths 
in  3  units?  in  4  units?  in  11  units? 

11.  In  one  pie  there  are.  ten  tenths;  how  many  tenths 
in  4  pies?  in  8  pies?  in  7  pies?  in  1  pie? 

12.  In  one  apple  there  are   7  sevenths;  how  many 
sevenths  in  8  apples?  in  3  apples?  in  6  apples?  in  2 
apples? 

13.  I  bought  3  apples  at  2  cents  apiece,  and  3  oranges 
at  4  cents  apiece;  how  much  did  I  give  for  all? 

14.  I  sold  3  quarts  of  chestnuts  for  11   cents  a  quart, 
and  then  gave  5  cents  of  what  I  received  to  a  poor  boy; 
what  did  I  have  left? 

15.  I  sold  8  quarts  of  walnuts  for  12  cents  a  quart, 
and  then  gave  8  cents  of  what  I  received  for  a  book; 
how  much  money  had  I  left? 

16.  How  much  will  8  slate  pencils  cost  at  2  cents 
apiece? 

17.  How  much  will  8  hats  cost  at  2  dollars  apiece? 

18.  How  much  will  8  pairs  of  boots  cost  at  3  dollars 
a  pair? 


b2  MULTIPLICATION 

LESSON   XXVII. 
WRITTEN  EXERCISES. 

165.  Multiply  34108643  by  5,  by  6,  by  7,  by  8. 
'166.  Multiply  470370864  by  5,  by  6,  by  7,  by  8. 
167.  Multiply  3780416413  by  5,  by  6,  by  7,  by  8. 
168."  Multiply  4067124  by  5,  by  6,  by  7,  by  8. 

169.  Multiply  86783407  by  5,  by  6,  by  7,  by  8. 

170.  Multiply  678341864  by  5,  by  6,  by  7,  by  8. 

171.  Multiply  478378062  by  5,  by  6,  by  7,  by  8. 

172.  Multiply  41834784  by  5,  by  6,  by  7,  by  8. 

173.  Multiply  683416803  by  5,  by  6,  by  7,  by  8. 

174.  Multiply  41860034  by  5,  by  6,  by  7,  by  8. 

175.  Multiply  3910670  by  5,  by  6,  by  7,  by  8. 

176.  Multiply  3004012  by  5,  by  6,  by  7,  by  8. 

177.  Multiply  550456  by  5,  by  6,  by  7,  by  8. 

LESSON   XXVIII. 

178.  Multiply  3098671  by  5,  by  6,  by  7,  by  8. 

179.  Multiply  3021916  by  5,  by  6,  by  7,  by  8. 

180.  Multiply  4896091  by  5,  by  6,  by  7,  by  8. 

181.  Multiply  3780689  by  5,  by  6,  by  7,  by  8. 

182.  Multiply  41969013  by  5,  by  6,  by  7,  by  8. 

183.  Multiply  6709062  by  5,  by  6,  by  7,  by  8. 

184.  Multiply  384022  by  5,  by  6,  by  7,  by  8. 

185.  Multiply  303402  by  5,  by -6,  by  7,  by  8. 

186.  Multiply  4030291  by  5,  by  6,  by  7,  by  8. 

187.  Multiply  3678641  by  5,  by  6,  by  7,  by  8. 

188.  Multiply  40307861  by  5,  by  6,  by  7,  by  8. 

189.  Multiply  30799186  by  5,  by  6,  by  7,  by  8. 


MULTIPLICATION. 


83 


LESSON    XXIX. 

TABLE. 

1  time    9  h        9. 

15  timfS  9  are  45. 

9  times  9  are     81. 

3  times  9  are  18. 

6  times  9  are  54. 

10  times  9  are     90. 

3  times  9  are  27. 

7  times  9  are  63. 

11  times  9  are     99 

4  times  9  are  38. 

8  times  9  are  72. 

12  times  9  are  108. 

Table  Exercise. 

10  +  9;   11  4-9; 

12  -f-  9;    13  +  9;  14+9;  15  +  9;  etc.    ' 

10  —  9;   11  —  9; 

12  —  9;   13  —  9     14  —  9;   15  —  9;  etc. 

10  x  9;  11  x  9; 

12  x  9;   13   x  9     14  x  9;   15  x  9;  etc. 

20  +  9;  21  +  9; 

22  +  9  ;    23  +  9     24  +  9  ;  25  +  9  ;  etc. 

20  —  9;  21  —  9; 

22  —  9;   23  —  9     24  —  9;   25  —  9;  etc. 

20  x  9;  21  x  9; 

22  x  9  ;   23  x  9     24  x  9  ;  25  x  9  ;  etc. 

30  +  9;  31+9; 

32  +  9  ;   33  +  9  ;   34  +  9  ;  35  +  9  ;  (tc. 

e  c.           etc. 

etc.            etc. 

e:c.            etc. 

BLACKBOARD    EXERCISES. 


0) 

1  12  0  4  3  2  6  5 

9   9999999 


10  9  8  7 
9999 


11 

9 


9999999   9   99   999 
1203465  12  10  7  11  98 


LESSON    XXX. 
WRITTEN  EXERCISES. 

1.  If  there  are  4  seats  in  a  row,  how  many  seats  in  9 
vows  ? 

2.  If  there  are  7  boys  in  a  class,  how  many  boys  in  9 
classes  of  the  same  size? 

3.  If  there  are  8  boys  and  girls  in  1   class,  how  many 
boys  and  girls  in  9  classes  of  the  same  size? 


84  MULTIPLICATION. 

4.  If  there  are  9  sheep  in  one  flock,  how  many  sheep 
in  12  flocks  of  the  same  size? 

5.  If  only  9  sheep  can  be  kept  in  one  pasture,  how 
many  sheep  can  be  kept  in  9  pastures  of  the  same  size? 

6.  There  are  7  horses  in  one  drove ;  how  many  horses 
in  9  droves  of  the  same  size? 

LESSON   XXXI. 
WRITTEN  EXERCISES. 

190.  Multiply  34678346  by  6,  by  7,  by  8,  by  9. 

191.  Multiply  410348  by  6,  by  7,  by  8,  by  9. 

192.  Multiply  340689  by  6,  by  7,  by  8,  by  9. 

193.  Multiply  348704  by  6,  by  7,  by  8,  by  9. 

194.  Multiply  328624  by  6,  by  7,  by  8,  by  9. 

195.  Multiply  304062  by  6,  by  7,  by  8,  by  9. 

196.  Multiply  340768  by  6,  by  7,  by  8,  by  9. 

197.  Multiply  438706  by  6,  by  7,  by  8,  by  9. 

198.  Multiply  380049  by  6,  by  7,  by  8,  by  9. 

199.  Multiply  341070  by  6,  by  7,  by  8,  by  9. 

200.  Multiply  41670  by  6,  by  7,  by  8,  by  9. 

201.  Multiply  3801264  by  6,  by  7,  by  8,  by  9. 

202.  Multiply  413042  by  6,  by  7,  by  8,  by  9. 

203.  Multiply  302098  by  6,  by  7,  by  8,  by  9. 

LESSON   XXXII. 

204.  Multiply  340672  by  6,  by  7,  by  8,  by  9. 

205.  Multiply  4370423  by  6,  by  7,  by  8,  by  9. 

206.  Multiply  6840709  by  6,  by  7,  by  8,  by  9, 

207.  Multiply  348604  by  6,  by  7,  by  8,  by  9. 

208.  Multiply  418340  by  6,  by  7,  by  8,  by  9. 

209.  Multiply  386412  by  6,  by  7,  by  8,  by  9. 


MULTIPLICATION.  85 

210.  There  are  56  sheep  in  one  flock  ;  how  many 
sheep  in  6  such  flocks  ?     What  is  the  value  of  each  flock 
at  7  dollars  a  head  ?     At  8  dollars  ?     At  9  dollars  ? 

211.  A  man  bought  384  pounds  of  sugar,  he  sold  290 
pounds ;    how  much  had  he  left  ?    How  much  did  he  re- 
ceive for  what  he  sold,  at  9  cents  a  pound  ?  What  is  the 
remainder  worth  at  8  cents  a  pound?  At  7  cents  a  pound? 

212.  A  merchant  sold  378  kegs  of  nails  at  9  dollars  a 
keg;   32  hundred  weight  of  iron  at  7  dollars  a  hundred; 
what  did  each  of  the  articles  come  to  ?     What  did  both 
come   to?     He   paid   away    1389    dollars;    how   much 
money  had  he  left  ? 

213.  There  are  63  boys  in  a  class;  each  boy  has  2 
hands;  each  boy  has  2  feet;  each  hand  has  4  fingers; 
each  ha  id  has  1  thumb ;  how  many  hands  have  all  the 
boys  ?     How   many  feet  ?     How   many  fingers  ?     How 
many  thumbs  ? 

214.  I   have  a  book  with  220  pages,  there  are  6  para- 
graphs on  each  page ;   there  are  9   lines  in  each  para- 
graph ;  there  are  8  words  in  each  line  ;   there  are,  on  an 
average,  5  letters  in  each  word  ;  how  many  paragraphs 
in  the  book  ?     How  many  lines  ?     How  many  words  ? 
How  many  letters  ? 

215.  A  grocer  sold   37   pounds  of  rice  at  8  cents  a 
pound  ;  46  pounds  of  sugar  at  9  cents  a  pound  :  what  did 
the  rice  come  to  ?      What  did  the  sugar  come  to  ?  What 
did  both  come  to  ?  What  did  one  cost  more  than  the  other  ? 

216.  A  boy  bought  37  pints  of  chestnuts  at  8  cents  a 
pint ;  46  pints  of  peanuts  at  9  cents  a  pint ;  what  did 
each  cost  ?     What  did  both  cost  ?     How  much  did  one 
cost  more  than  the  other  ? 


86 


MULTIPLICATION. 


LESSON     XXXIII, 

TABLE. 

0 

times 

10 

are 

0.           0 

times 

11 

are 

0. 

1 

times 

10 

are 

10, 

1 

times 

11 

are 

11. 

2 

times 

10 

are 

20. 

2 

times 

11 

are 

2*2 

3 

times 

10 

are 

30. 

3 

times 

11 

are 

53 

4 

times 

10 

are 

40. 

4 

times 

11 

are 

44. 

5 

times 

10 

are 

50. 

5 

times 

11 

a\e 

55. 

6 

times 

10 

are 

60. 

6 

times 

11 

are 

66. 

7 

times 

10 

are 

70. 

7 

times 

11 

are 

77. 

8 

ti.aes 

1C 

are 

80. 

8 

times 

11 

nre 

88. 

9 

times 

10 

are 

90, 

9 

limes 

11 

are 

99. 

10 

times 

10 

arc 

100. 

10 

times 

11 

are 

110. 

11 

times 

10 

ar  ' 

110. 

11 

times 

11 

are 

121. 

12 

times 

10 

are 

120. 

12 

times 

11 

are 

132. 

BLACKBOARD    EXERCISES. 

(i) 

0 

1    12 

2 

11 

3    10      4 

9      5 

8 

G 

7 

10 

10    10 

10 

10 

10    10    10 

10    10 

10 

10 

10 

p?) 

1   4   2   3   G   5   8   7  10  11   9   0  12 
11  11  11  11  11  11  11  11  11  11  11  11  11 


LESSON    XXXIV. 
MENTAL  EXERCISES. 

1.  What  cost  10  apples  at  2  cents  apiece? 

2.  What  cost  10  melons  at  8  cents  apiece? 

3.  What  cost  10  citrons  at  ten  cents  apiece? 

4.  What  cost  12  pine-apples  at  10  cents  apiece? 

5.  What  cost  9  squashes  at  10  cents  apiece? 

6.  What  cost  11  cabbages  at  10  cents  apiece? 

7.  What  cost  10  loaves  of  bread  at  5  cents  a  loaf? 


MLLTII'LlC/VTlOtf. 

~.  WTi«u  cost  11  oranges  at  four  cents  apiece? 

9.  If'  there  are   11    elevenths  in  one  unit,  how  many 
elevenths  in  9  units? 

10.  If  there  are  7  days  in  one  week,  how  many  days 
in  12  weeks? 

11.  If  there  are  12  ounces  in  1   pound,  Troy  Weight, 
how  many  ounces  in  1 1  pounds,  Troy  Weight? 

12.  If  there  are  5  fifths  in  one  unit,  how  many  fifth* 
in  11  units? 

13.  Five  times  11,  added  to  7,  are  how  many? 
1  \.  Four  times  11,  added  to  o,  are  how 

15.  9  times  11,  less  5,  are  how  many? 

16.  o  times  11,  less  8,  are  how  many? 

17.  12  times  11,  less  7,  are  how  many? 

18.  8  times  ll,t  less  10,  are  how  many? 

19.  3  times  11,  less  3,  are  how  many? 

20.  2  times  11,  less  20,  are  how  many? 

21.  2  times  8,  less  5,  are  how  many? 

22.  4  times  8,  plus  9,  are  how  many? 

23.  8  times  7,  plus  3,  are  how  many? 

24.  5  fimes  9,  plus  7,  are  how  many? 

25.  4  times  11,  less  3,  are  how  many? 

26.  8  times  6,  less  18,  are  how  many? 

27.  6  times  7,  less  4,  are  how  many? 

28.  8  times  9,  less  3$  are  how  many? 

29.  5  times  6,  less  8,  are  how  many? 

30.  3  times  7.  less  6,  are  how  many? 

31.  4  times  11,  less  20,  are  how  many? 

32.  9  times  11,  plus  20,  are  how  many? 


98  MULTIPLICATION. 

LESSON    XXXV. 

• 

WRITTEN  EXERCISES. 

217.  Multiply  3006084  by  11,  by  12,  by  13,  by  14. 

218.  Multiply  3908706  by  13,  by  14,  by  15,  by  16. 

219.  Multiply  4198307  by  15,  by  16,  by  17,  by  18. 

220.  Multiply  4186983  by  17,  by  18,  by  19,  by  20. 

221.  Multiply  4089678  by  19,  by  20,  by  21,  by  22. 

222.  Multiply  4183076  by  21,  by  22,  by  23,  by  24. 

223.  Multiply  498347  by  23,  by  24,  by  25,  by  26. 

224.  Multiply  6783416  by  25,  by  26,  by  27,  by  28. 

225.  Multiply  4189674  by  27,  by  28,  by  29,  by  30. 

226.  Multiply  3786413  by  29,  by  30,  by  31,  by  32. 

227.  Multiply  4678346  by  31,  by  32,  by  33,  by  34. 

228.  Multiply  41867834  by  33,  by  34,  by  35,  by  36. 

229.  Multiply  34867834  by  35,  by  36,  by  37,  by  38. 

LESSON    XXXVI. 

230.  Multiply  1342672  by  39,  by  40,  by  41,  by  42. 

231.  Multiply  4186834  by  43,  by  44,  by  45,  by  46. 

232.  Multiply  2189672  by  47,  by  48,  by  49,  by  50. 

233.  Multiply  89168397  by  51,  by  52,  by  53,  by  54. 

234.  Multiply  4108692  by  55,  by  56,  by  57,  by  58. 

235.  Multiply  9878382  by  59,  by  60,  by  61,  by  62. 

236.  Multiply  467834  by  63,  by  64,  by  65,  by"  66. 

237.  Multiply  38416  by  67,  by  68,  by  69,  by  70. 

238.  Multiply  47034  by  71,  by  f2,  by  73,  by  74. 

239.  Multiply  37068  by  75,  by  76,  by  77,  by  78. 

240.  Multiply  4070864  by  79,  by  80,  by  81,  by  82. 

241.  Multiply  3070864  by  83,  by  84,  by  85,  by  86. 

242.  Multiply  408706  by  87,  by  88,  by*89,  by  90. 


MULTIPLICATION. 


LESSON   -XXXVII. 


9  times  12  are  108 

10  times  12  are  120 

11  times  12  are  132 

12  times  12  are  144 


'I'ab, 

10  x  12;  11  x  12;   12  x  12; 
20  x  12;   21  x  12;   22  x  12; 

Q  A     v ..     1  o  .     O1      ^,     1O.      CO     .  ,     1  *•>  . 


Table  Exercise. 


etc. 


etc. 


12 


etc. 


;  44  x  12;  45  x  12;  etc. 
;  54  x  12;  55  x  12;  etc. 
etc.  etc. 


BLACKBOARD    EXERCISES. 


(1) 

0  1   2  10  3  11   9  4  8  -5  7  6  12 
12  12  12  12  12  12  12  12  12  12  12  12  12 

(2) 

12  1-2  12  12  12  12  12  12  12  12  12  12  12 

1  o  12  2  0  9  10  8  6  7  5  11  4 


LESSON   XXXVIII. 
MENTAL  EXERCISES. 

1.  If  in  each  lesson  you  answer  12  questions  correctly, 
bow  many  correct  answers  would  you  give  in  12  lessons? 

2.  If  9  gallons  of  water  run  into  a  cistern  in  one  min- 
Hte,  how  many  gallons  will  run  into  it  in  12  minutes? 

3.  A  ship  can  sail  8  miles  in  an  hour ;  how  many  miles 
can  she  sail  in  12  hours? 

7 


90  MULTIPLICATION. 

,      4.  There  are  4  soldiers  in  one  rank ;  how  many  soldiers 
in  12  ranks? 

5.  At  3  cents  apiece  what  will  12  lemons  cost? 

6.  At  12  cents  apiece  what  will  2  pine-apples  cost? 

7.  There  are  5  school-hours  in  a  day ;  how  many  school- 
hours  in  12  days? 

8.  There  are  11  yards  in  a  piece  of  cloth;  how  many 
yards  in  12  pieces  of  the  same  length? 

9.  There  are  12  twelfths  in  a  unit;  how  many  twelfths 
in  7  units?  in  8  units?  in  5  units? 

10.  If  one  lead  pencil  cost  4  cents,  what  will  12  lead 
pencils  cost? 

11.  If  you  receive  12  apples  to-day  and  12  to-morrow, 
how  many  will  you  receive  on  both  days? 

12.  There  are  6  working  days  in  a  week;  how  much 
can  you  earn,  if  you  earn  12  cents  each  day? 

13.  What  cost  11  quarts  of  chestnuts  at  12  cents  a 
quart  ? 

14.  Butter  is  12  cents  a  pound;  what  will  9  pounds 
cost? 

15.  If  a  butcher  pays  9  dollars  a  head  for  sheep,  how 
much  must  he  pay  for  12  head? 

16.  Rice  is  11  cents  a  pound;  what  will  12  pounds 
cost? 

17.  There  are  5  fifths  in  1   unit;  how  many  jifths  in 
12  units; 

18.  There  are  3  thirds  in  an  orange;  how  many  thirds 
in  12  oranges? 

19.  There    are    7  sevenths   in    an    apple;    how  man}' 
sevenths  in  12  apples? 


MULTIPLICATION.  91 

LESSON    XXXIX. 

WRITTEN  EXERCISES. 

243.  Multiply  3470864  by  1,  by  20,  by  300,  by  4000. 

244.  Multiply  41307G8  by  5,  by  60,  by  700,  by  8000. 

245.  Multiply  41890673  by  9,  by  90,  by  900,  by  9000, 

246.  Multiply  4983904  by  l,by  11,  by  101,  by  1001. 

247.  Multiply  4683419  by  2,  by  22,  by  202,  by  2002. 

248.  Multiply  9786427  by  3,  by  30,  by  330,  by  3300. 

249.  Multiply  4186438  by  4,  by  44,  by  444,  by  4044. 

250.  Multiply  9678673  by  5,  by  50,  by  505,  by  5500. 

251.  Multiply  4418684  by  3,  by  30,  by  207,  by  5001. 

252.  Multiply  6968034  by  4,  by  45,  by  406,  by  3101. 

253.  Multiply  4186372  by  6,  by  37,  by  206,  by  3202. 

254.  Multiply  4186302  by  9,  by  11,  by  601,  by  3701. 

255.  Multiply  4860960  by  2,  by  12,  by  402,  by  4008. 

LESSON   XL. 

256.  Multiply  4083786  by4/by  24,  by  302,  by  6080. 

257.  Multiply  4183467  by  2,  by  60,  by  300,  by  2008. 

258.  There  are  36  yards  in  one  piece  of  cloth ;  how 
many  yards  in  12  such  pieces  ? 

259.  If  a  butcher   pays   12  dollars  a  head  for  sheep, 
how  much  will  378  sheep  cost  him  ? 

260.  Bought  6783  pounds  of  rice  at  15  cents  a  pound; 
what  did  it  come  to  ? 

261.  If  a   man   owed    3789   dollars,  and  having  paid 
2786  dollars,  how  much  does  he  still  owe  ? 

262.  There  are  365   daysjin    one   vear;    Low  many 
days  in  21  years  ? 


92  MULTIPLICATION. 

233.   There  are  24  hours  in.  a  day ;  how  many  hours 
in  365  days  or  1  year  ? 

264.  There  are  30  days  in  1  month ;  how  many  days 
in  42  months  ? 

265.  There  are  4  farthings  in  one  penny;  how  many 
farthings  in  240  penes  ? 

266.  There  are  12  pence  in  one  shilling ;  how  many 
pence  in  640  shillings  ? 

267.  There  are  21  shillings  in  one  guinea;  how  many 
shillings  in  325  guineas  ? 

268.  In  one  pound  avoirdupois  there  are   16  ounces ; 
how  many  ounces  in  372  pounds  ? 

269.  There  are   100   pounds   in  one  hundred  weight; 
how  many  pounds  in  327  hundred  weight  ? 

270.  In   one   ton  there  are  2000  pounds ;   how  many 
pounds  in  376  tons  of  coal  ? 

271.  A  barrel  of  flour  weighs  196  pounds  ;  how  many 
pounds  in  370  barrels  ? 

272.  In  a  barrel  of  beef,  fish,  or  pork,  there  are  200 
pounds  ;  how  many  pounds  in  380  barrels  ? 

273.  I  bought  47  barrels  of  salt ;  if  each  barrel  weighs 
280  pounds,  how  many  pounds  did  I  buy  in  all  ? 

274.  This  room   is  21  feet  long ;   how   many  inches 
long  is  it  if  there  are  12  inches  in  a  foot  ? 

275.  This  room  is   18   feet  wide;  how  many  inches 
wide  is  it  ? 

276.  The  ceiling  is  8  fe8t  high,  how  many  inches  high 
is  it? 

277.  There  are  3  feet  in  a  yard ;  the  street  is  18  yards 
wide  ;  how  many  feet  is  it  ? 


MULTIPLICATION.  93 

278.  There  are  320  rods  in  a  mile  ;  how  many  rods  in 
27  miles  ? 

279.  About  3  feet  make  a  step,  or  a  pace;   a  man 
in  walking  across  the  garden,  took  36  steps;   how  many 
feet  long  is  it  ? 

280.  About  1760  steps  make  a  mile  ;  how  many  steps 
in  3  miles  ? 

281.  Thomas  lived   2  miles  from  school ;  how  many 
steps  must  he  take  each  day  to  go  and  return  ? 

282.  His  little  brother  takes  2  steps  while  Thomns 
takes  one,  how  many  steps  must  he  take  to  go  to  school 
and  return  ? 

283.  There  are  4  quarts  in  a  gallon ;  how  many  quarts 
in  46  gallons  of  molasses  ? 

284.  Four  gills  make  a  pint;  how  many  gills  in  37 
pints  of  milk  ? 

285    In  a  quart  there  are  2  pints ;  how  many  pints  in 
483  quarts  of  vinegar  ? 

286.  In  a  peck  there  are  8  quarts ;  how  many  quarts 
in  278  pecks  of  beans  ? 

287.  In  a  bushel  there  are  4  pecks  ;  how  many  pecks 
in  467  bushels  of  apples  ? 

288.  In  a  minute   there  are  60  seconds;  how  many 
seconds  in  380  minutes  ? 

289.  In  an  hour   there   are  60  minutes;  how  many 
minutes  in  24  hours  or  a  day  ? 

290.  In  a  week  there  are  7  days ;   how  many  days  in 
52  weeks  ? 

291.  If  John  can  solve    ten    problems  a   day,   how 
many  problems  can  he  solve  in  a  school  year  of  200 
days? 


94  MULTIPLICATION. 

292.  A  dealer  received  an  order  for  374  barrels  of 
beef;  he    had  only  276  barrels    on   hand;  how   many 
barrels  more  will  he  require  to  fill  the  order  ? 

293.  The  sales  of  my  store  for  January  amounted  to 
1837  dollars,  and  only  897  dollars  in  February  ;  how 
much  did  I  sell  more  isi  January  than  in  February? 

294.  A  gardener  received  in  1867,  4271  dollars  for 
vegetables,  his  expenses  were  1288  dollars;  what  were 
his  profits  ? 

295.  If  I  owe  3864  dollars  and  pay  2187  dollars,  how 
much  do  1  still  owe  ? 

296.  At  the  office  of  a  Baltimore  paper  157  reams  of 
paper  are  used  daily ;  at  that  rate  how  much  paper  will 
be  required  to  last  307  days  ? 

297.  The  annual  imports  at  Charleston,  S.  C.,  amount 
to  983864   dollars,    the  exports    of  cotton    amount  to 
1713465  dollars;  how  much  does  the  annual  exports  ex- 
ceed the  imports  ? 

298.  In  1860,  in  North  Carolina,  the  real  estate  was 
valued  at    116,366,573  dollars;  in    South  Carolina,    it 
was  valued  at  129,772,684  dollars;  how  much  did  the 
real  estate  in  South  Carolina  exceed  in  value    the  real 
estate  in  North  Carolina  ? 

199.  Delaware  contains  an  area  of  2120  square  miles, 
and  Maryland  9356  square  miles ;  how  much  larger  is 
Maryland  than  Delaware  ? 

300.  Virginia  contains  61322  square  miles,  Georgia, 
58000  sq.  m. ;  Florida,  59268  sq.  m. ;  Alabama,  50722 
sq.  m.;  Louisiana,  46431  sq.  m. ;  Texas,  237321  sq.  m.  ; 
Mississippi,  47156  sq.  m. ;  Arkansas,  52198  sq.  m., 
Tennessee,  45600  sq.  m. ;  how  many  square  miles  in  all 
of  the  above  States  ? 


SECTION  V. 
LESSON   I. 

I  divided  10  apples  equally  between  2  boys ;  how 
many  did  each  boy  receive  ? 

FORMULA. — If  2  boys  received  10  apples,  1  boy  received  one-half 
of  10  apples,  which  is  5  apples;  therefore,  each  .boy  received  5  apples. 

1.  There  are  24  bushels  of  potatoes  in  a  pile ;  how 
many  barrels  will  it  take  to  hold  them  if  each  barrel 
holds  2  bushels  ? 


96  DIVISION. 

FORM.— Since  each  barrel  holds  2  bushels,  it  will  take  as  many  bar- 
rels as  2  bushels  (can  be  subtracted  from)  are  contained  times  in  24 
bushels,  which  is  12 ;  hence  it  will  take  12  barrels  to  hold  the  potatoes 

2.  If  I  divide  12  nuts  between  2  boys,  how  many  nuts 
will  each  boy  receive? 

3.  2  girls  have  14  cents;  how  many  is  that  apiece? 

4.  8  chestnuts  are  divided  into  2  equal  parts;  how 
many  nuts  in  each  part? 

5.  18  apples  are  divided  into  2  equal  parts;  how  many 
apples  in  each  part? 

6.  If  2  dimes  contain  20  cents,  how  many  cents  does 
1  dime  contain? 

7.  I  wish  to  divide  12  peaches  equally  between  my  2 
children;  how  many  must  I  give  to  each? 

8.  I  have  4  marbles,  and  I  wish  to  put  an  equal  num- 
ber into  each  of  my  two  pockets;  how  many  must  I  put 
into  each? 

9.  I  have  2  oranges  which  I  wish  to  divide  equally 
between  Charles  and  Henry;  how  many  must  I  give 
each? 

10.  If  2  boys  receive  6  oranges,  how  many  does  one 
receive? 

11.  2  men  receive  16  dollars;  how  much  does  one  man 
receive? 

12.  2  men  cut  18  cords  of  wood  in  a  week;  how  much 
does  one  of  the  men  cut? 


*  The  teacher  should  not  fail  to  explain  to  the  class  what  is  meant  by  one- 
kalfi  one-t/iir't,  one-fiflk,  one-n>ntn<  &c  The  expression,  one-half  of  a  number, 
really  means  that  the  number  is  to  be  MULTIPLIED  BY  ont-tialf,  *;of"  in  this 
place,  meaning  TIMES,  and  the  product  of  the  multiplication  is  equal  to  one  part, 
of  a  number  which  is  divided  into  two  equal  parts.  The  expression,  one-Half 
tf  a  number,  is  so  familiar  to  eyery  child  thac  we  prefer  it  in  this  form  of  divi- 
sion to  any  other 


DIVISION.  97 

13-2  pounds  of  sugar  cost  14  cents;  what  did  1  pound 
cost? 

14.  2  pounds  of  cheese  cost  12  cents;  what  did  one 
pound  cost? 

15.  2  pounds  of  rice  cost  10  cents;  what  did  one  pound 
cost? 

LESSON  m. 
WRITTEN  EXERCISES, 

In  which  each  figure  of  the  Dividend  is  a  multiple  of  the  Divisor. 
(1)  (2)  (3)  (4)  (5) 

2)428612  2)208462  2)242680  2)424826  2)462860 


(6)       (7)        (8)        (9)  *  (10) 
2)428622  2)2046486  2)2064862  2)626882  2)62484660 

(11)       (12)       (13)       (14)  (15) 

2)468286  2)624286  2)624468  2)268246  2)2462842 

LESSON  IV. 

(16)       (17)       (18)       (19)  (20) 

2)24486024  2)2482486  2)2426824  2)4628824  2)40608024 


(21)        (22)        (23)        (24)       (25) 
2)8060242  2)2064248  2)8426842   2)2482642  2)624280 


(26)       (27)       (28)       (29)        (30) 
*)2808642  2)4260842  2)6248264  2)2622278   2)4246824 


(31)       (32)        (33)       (34)       (35) 
2)24824268  2)42684284  2)624824682  2)24282486  2)24128642 


98 


DIVISION. 


LESSON   V. 

TABLE. 

1  in    1,    once. 

2  in    2,    once. 

3  in    3,    once. 

1  in    2,    twice. 

2  in    4,    twice. 

3  in    6,    twice. 

1  in     3,     3  times. 

2  in      6,     3  times. 

3  in     9,     3  times. 

1  in    4,     4  times. 

2  in     8,     4  times. 

3  i»  12,     4  times. 

1  in     5,     5  times. 

2  i'i  10,      5  times. 

3  in  15,     5  times. 

1  in     6,     6  times 

2  in  12,     6  times. 

3  in  18,     6  times. 

1  in     7,     7  times. 

2  in  14,      7  times. 

3  in  21,     7  times. 

1  in     8,     8  times. 

2  in  16,      8  times. 

3  in  24,     8  times. 

1  'm     9,     9  times. 

2  in  18,      9  times. 

3  in  27,     9  times. 

1  in  10,  10  times. 

2  in  20,  10  times. 

3  in  30,  10  times. 

1  in  11,  11  times. 

2  in  22,  11  times. 

3  in  33,  11  times. 

1  in  12,  12  times. 

2  in  24,  12  times. 

3  in  36,  12  times. 

BLACKBOARD    EXERCISES. 
CD 

3)3  10  4  9  13  1  12  8  5  7  6  11  2 

(2) 

3)14  21  18  24  20  25  16  26  19  2-3  17  22  15 


LESSON    VI. 
MENTAL  EXERCISES. 

1.  If  you  were  to  divide  6  cents  equally  among  3  boys, 
how  many  cents  would  you  give  to  each  boy? 

SOLUTION. — (See  solution,  Lesson  II.,  Example  1.) 

2.  If  a  stick  be  nine  feet  long,  and  you  cut  it  into  three 
equal  parts,  how  many  feet  long  will  each  part  be? 

3.  A  boy  wished  to  divide  12  marbles  into  three  equal 
piles ;  how  many  marbles  must  there  be  in  each  pile  ? 

4.  Henry  had  21   peach-stones  which  he   planted  i» 
rows  of  three  each;  how  many  rows  were  there? 


DIVISION.  99 

5.  A  teacher  had  in  her  school  24  scholars  whom  she 
divided  into  classes  of  three  each;   ho\v  many   elates 
were  there  in  the  school? 

6.  If  you  should  make  27  marks  on  your  slate,  and 
should  separate  them  into  groups  of  three  each,  how  many 
groups  would  there  be? 

7.  If  3  yards  of  twist  cost  30  cents,  what  does  one 
yard  cost? 

8.  If  3  pounds  of  sugar  cost  27  cents,  what  does  one 
pound  cost? 

9.  If  3  books  cost  27  cents,  what  does  one  book  cost? 

10.  If  3  sheep  cost  36  dollars,  what  does  one  sheep 
cost? 

11.  I  gave  21  cents  for  3  melons;  how  much  did  one 
melon  cost  me? 

12.  I  gave  18  cents  for  three  bottles  of  ink;  how  much 
did  one  bottle  cost? 

13.  A  mail  bought  3  pigs,  for  which  he  gave  24  dol- 
lars; how  much  did  one  pig  cost  him? 

14.  A  boy  sold  3  quarts  of  chestnuts  for  15  cents;  how 
much  did  he  receive  for  1  quart? 

15.  A  farmer  sold  3  bushels  of  apples  for  6  shillings; 
how  much  did  he  receive  a  bushel? 

16.  If  a  man  drink  3  quarts  of  water  in  3  half-days, 
Vow  much  will  he  drink  in  one  half-day? 

17.  If  a  butcher  pays  12  dollars  for  3  sheep,  how  much 
fe  that  a  head? 

18.  If  three  hats  cost  9  dollars,  how  much  will  one  hat 
rost  ? 

19.  If  a  man  earns  12  dollars  in  3  weeks,  bow  mucb 
will  he  earn  in  one  week? 


100 


DIVISION. 


20.  There  are  15  cents  in  3  half-dimes;  how  many 
cents  in  1  half-dime? 

21.  There  are  18  single  things  in  3  half-dozens;  how 
many  single  things  in  one  half-dozen? 

22.  There  are  21  days  in  three  weeks;  how  many  day? 
in  one  week? 

WESSON  vn. 
*WRITTEX  EXERCISES, 
.   In  which  each  partial  Dividend  is  not  a  multiple  of  the  Divisor. 

(36)  (37)  (38)  (39)  (40) 

3)4363093     3)703600993     3)160960309     3)73069306     3)10369306 


(41)  (42)  (43)  (44)  (45) 

3)73609936   3)160360309   3)136091369   3)19690039    3)139609096 


(46)  (47)  (48)  (49)  (50) 

3)13700916     3)439066909    3)136099130    3)43329096    3)3966093 


LESSON    VIII. 

(51)       (52)      (53)  (54)      (55) 

2)15799339  2)1357957  2)351795  2)537955  2)3159755 

(56)        (57)        (58)  (59)       (60) 

2)31579399   2)53135799   2)31579771  2)3579135   2)35151714 

(61)        (62)        (63)  (64)       (65) 

2)3579557   2)135317935   2)35179573  2)35719185  2)5379375 


*  NOTE  FOR  THE  TEACHER — The  teacher  should  take  occasion  to  explain  thi 
method  of  dividing  when  each  figure  is  net  a  multiple-,  before  requiring  the  per 
fomanee  of  these  exercises 


DIVISION. 


101 


LESSON   IX. 


4  in    4,  once. 

4  in    8,  twice. 

4  in  12,  3  times. 

4  in  16,  4  tini33. 


4  in  20,  5  times. 

4  in  24,  6  times. 

4  in  28,  7  times. 

4  in  32,  8  times. 

Table  Exercise. 


4  in  36, 
4  in  40, 
4  i»  44, 
4  in  48, 


9 

10 
1  1 
12 


times. 
times. 
times. 


1  is  0  times  4  and  1  over. 

2  i*  0  times  4  and  2  over. 

3  is  0  times  4  and  3  over. 

5  is  OUC 3      4  and  1  over. 

6  is  OHC3      4  and  2  ove  . 

etc. 


10 

-4  = 

? 

11 

-7- 

4 

20 

-4  = 

9 

21 

-f- 

4 

30 

-4  = 

? 

31 

_:_ 

4 

40 

-4  = 

? 

41 

4. 

4 

50 

-4  = 

V 

51 

-f- 

4 

efc. 

£/<?. 

etc. 
etc. 
etc. 


BLACKBOARD  EXERCISES. 


4)14  21  23  22  25  17  26  19  27  18  29  15 


4)30  37  45  38  39  33  41  35  42  34  43  31 


LESSON   X. 
MENTAL  EXERCISES, 

1.  At  4  cents  a  jard  how  many  yards  of  ribbon  may 
be  bought  for  20  cents? 

^SOLUTION. — If  1  yard  of  ribbon  can  be  bought  for  4  cents,  as 
many  yards  can  be  bought  for  20  cents,  as  4  cents  are  contained 
times  in  20  cents,  which  are  5. 

Therefore,  if  1  yard  of  ribbon  can  be  bought  for  4  cents,  6 
yards  can  be  bought  for  20  cents. 

*  NOTE  FOR  THE  TEACHER.— The  teacher  ehould  nor  fail  to  explain  to  the  pu 

Blls  the  difference  between  the  two  forms  of  Division— the  one  which  divides  the 
ividend  intr  as  many  parts  as  there  are  units  in  the  Divisor,  (see  Lesson  II. 
imd  VI  .  Section  V.,)and  the  other,  which  sxibtracts  the  Divisor  from  the  Divi- 
dend a  certain  number  of  times,  (see  Introduction.)  Let  particular  attention 
be  given  to  the  difference  between  the/onwj  of  solution. 


102  DIVISION. 

2.  At  4  dollars  a  yard  how  many  yards  of  broadcloth 
can  be  bought  lor  12  dollars?  for  16  dollars?  for  32  dol- 
lars? for  28  dollars? 

3.  At  4  cents  a  piece  how  many  pieces  of  tape  can  be 
bought  for  20  cents?  for  8  cents?  for  40  cents?  for  48 
cents  ? 

4.  I  have  40  melons ;  how  many  baskets  will  they  fill 
if  I  can  put  only  4  melons  in  a  basket? 

5.  I  have  4 J  dollars ;  how  many  boys  can  I  hire  if  I 
give  each  boy  4  dollars? 

6.  In  4  pecks  there  is  one  bushel;  how  many  bushels 
in  36  pecks?  in  44  pecks?  in  48  pecks?  in  16  pecks? 

7.  In  4  quarts  there  is  one  gallon;  how  many  gallons 
in  24  quarts?  in  28  quarts?  in  32  quarts? 

8.  How  many  pounds  of  rice  can  I  buy  for  36  cents  at 
•4  cents  per  pound? 

9.  How  many  pencils  can  I  buy  for  40  cents  at  4  cents 
apiece  ? 


LESSON   XI. 
WRITTEN1  EXERCISES. 

In  which  each  figure  of  the  Dividend  may  or  may  not  be  a  multi- 
ple of  the  Divisor. 

66.  Divide  3418067803  by  2,  by  3,  by  4. 

67.  Divide  6780346783  by^2,  by  3,  by  4. 

68.  Divide  460780346  by  2,  by  3,  by  4. 

69.  Divide  418786437  by  2,  by  3,  by  4. 

70.  Divide  416078341  by  2,  by  3,  by  4. 

71.  Divide  62413724  by  2,  by  3,  by  4. 


DIVISION.  103 

LESSON    XII. 

72.  I  have  327  oranges,  and  sell  311 ;  how  many  re- 
main ?     How  much  shall  I  receive  at  8  cents  each  ?     If 
I  divide  the  money  among  4  little  boys;    how  much  will 
each  have  ? 

73.  At  2  cents  each  how  many  apples  can  I  buy  for 
4344  cents  ?      How   many  peaches  at  3   cents    each  ? 
How  many  oranges  at  4  cents  each  ? 

74.  At  2  dollars  a  day  how  many  days  work  can  I  hire 
for  346  dollars  ?  For  496  dollars  ?  For  3176  dollars? 

75.  At  3  cents  a  yard  how  many  yards  of  tape  can  I 
buy  for  381  cents  ?     For  573  cents  ?     For  4962  cents  ? 

76.  There  are  4  pecks  in  a  bushel ;   how  many  pecks 
in  3844  bushels?  In  7688  bushels?  In  15376  bushels? 

77.  There  are  4  quarts  in  a  gallon  ;  how  many  gallons 
in  132  quarts  ?     In  396  quarts  ?    In  792  quarts  ? 

78.  How  many  pounds  of  rice,  at  4  cents  a  pound,  can 
I  buy  for  3672  cents  ?  For  7344  cents  ?  For  14688  cts.  ? 

79.  How  many  hats  can  be  bought  at  4  dollars  apiece 
for  64  dollars  ?     For  192  dollars  ?     For  1152  dollars  ? 

80.  There  are  3  feet  in  1  yard ;  how  many  feet  in  27 
yards  ?     In  16  yards  ?     In  29  yards  ? 

81.  In  3  feet  there  is  1  yard ;  how  many  yards  in  69 
feet  ?     In  276  feet  ?     In  828  feet  ? 

82.  If  4  cannon  balls  weigh  108  pounds,  how  much 
will  one  of  the  'balls  weigh  ?     If  3  weigh  103  pounds  ? 
If  4  weigh  388  pounds  ? 

83.  If  4  poles  of  equal  length  measure  44  feet,  what 
is  the  length  of  each  of  the  poles  ?  If  they  measure  132  ? 
If  they  measure  264  feet  ? 


104 


DIVISION. 


LESSON  XIII. 

TABLE. 

5  in 

5, 

once 

5 

in  25,    5  times. 

5  in 

45, 

9 

times. 

5  in 

10 

twice. 

5 

in  30,    6  times. 

5  in 

50 

10 

times. 

5  in 

15 

3  times. 

5 

in  35,    7  times. 

5  in 

55 

11 

times. 

5  in 

23, 

4  times. 

5 

in  40,    8  times. 

5  in 

60, 

12 

times. 

Table  Exercise. 

lis 

Ot 

mas  5 

and 

1 

over. 

10+-5;   11-^-5 

;  12-5-5 

;  etc. 

2  >s 

0  tinus  5 

and 

2 

over. 

20  -5-  5  ;  21-5-6 

;  22 

-T-  5 

;  etc. 

3  is 

0  tim33  5 

and 

3 

over. 

30  -5-  5  ;  31  -f-  5 

;  32 

-r-  5 

;  etc. 

4  13 

0  times  5 

and 

4 

over. 

40  -v-  5  ;  41-^-5 

;  42 

-5-5 

;  etc. 

6  is 

011C3      5 

and 

1 

over. 

50  -f-  5  ;  51  -f-  5 

;  52 

-5-5 

;  etc. 

etc. 

etc. 

etc. 

etc. 

BLACKBOARD    EXERCISES. 


(1) 

5)17  24  23  26  22  27  18  28  21  29  19  31  16 


5)32  41  39  42  38  43  34  46  37  44  36  47  33 


LESSON    XIV. 
MEXTAL  EXERCISES. 

1.  How  many  barrels  of  flour  at  5  dollars  a  barrel  can 
you  buy  for  10  dollars? 

SOLUTION. — (See  solution,  Lesson  X.,  Section  V.) 

2.  How  many  rows  of  pegs  will  be  wanted  to  hang  up 
20  hats,  if  5  hats  are  hung  in  each  row? 

3.  How  many  quarts  of  vinegar  can  be  bought  for  15 
cents,  jf  1  quart  costs  5  cents? 

4.  How  many  quarts  of  milk  can  be  bought  for  25 
tents,  when  milk  is  5  cents  a  quart? 


DIVISION.  105 

5.  At  5  shillings  a  pound  how  many  pounds  of  tea  can 
be  bought  for  60  shillings? 

6.  At  5  cents  a  bunch  how  many  bunches  of  tooth- 
picks can  be  purchased  for  35  cents? 

7.  At  5  cents  apiece  how  many  tops  can  I  buy  for  10 
cents? 

8.  How  many  five-cent  pieces  are  required  to  make  25 
cents  or  a  quarter  dollar?     How  many  cents  in  a  quarter 
dollar? 

9.  How  many  five-cent  pieces  are  required  to  make 
one  dime  or  10  cents?     How  many  cents  in  one  dime? 

10.  At  5  dollars  a  barrel  how  many  barrels  of  flour 
can  I  buy  for  15  dollars? 

11.  At  5  dollars  a  pair  how  many  pairs  of  boots  can 
1  buy  for  30  dollars?  for  60  dollars?  for  45  dollars? 

12.  I  have  50  dollars  to  lay  out  in  vests  at  5  dollars 
apiece;  how  many  can  I  buy? 

13.  I  have  55  dollars  to  lay  out  in  sheep  at  5  dollars 
a  head;  how  many  can  I  buy? 

14.  A  merchant  had  a  piece  of  broadcloth  containing 
40  yards,  which  he  wished  to  make  into  boys'  suits,  each 
suit  to  contain  5  yards;  how  many  coats  could  he  make? 

15.  5  pieces  of  tape  cost  20  cents;  how  much  did  one 
of  the  pieces  cost? 

16.  On  5  pages  of  print  there  are  60  mistakes;  how 
many  mistakes  on  one  of  the  pages? 

17.  In  5  days  I  pay  55  cents  for  milk;  how  much  is 
that  a  day? 

18.  How  much  will  8  apples  cost  at  3  cents  apiece? 

19.  If  I  have  8  apples  and  give  away  3,  how  many 
will  T  have  left? 


106  DIVISION. 

2C.  If  I  have  8  apples  and  my  mother  gives  me  8 
more,  how  many  shall  I  then  have? 

21.  John  had  3  apples,  then  he  gave  away  2,  his 
mother  then  gave  him  7 ;  how  many  did  he  then  have  ? 

LESSON   XV. 
WRITTEN  EXERCISES. 
84  Divide  3678304  by  2,  by  3,  by  4,  by  5. 

85.  Divide  41676713  by  2,  by  3,  by  4,  by  5. 

86.  Divide  6786783  by  2,  by  3,  by  4,  by  5. 

87.  Divide  5678376  by  2,  by  3,  by  4,  by  5. 

88.  Divide  4786894  by  2,  by  3,  by  4,  by  5. 

89.  Divide  4167183  by  2,  by  3,  by  4,  by  5. 

90.  Divide  4186713  by  2,  by  3,  by  4,  by  5. 

91.  Divide  3718671  by  2,  by  3,  by  4,  by  5. 

92.  Divide  4100671  by  2,  by  3,  by  4,  by  5. 

93.  Divide  418767  by  2,  by  3,  by  4,  by  5. 

LESSON    XVI. 

94.  Divide  4867183  by  2,  by  3,  by  4,  by  5. 

95.  Divide  67183714  by  2,  by  3,  by  4,  by  5. 

96.  Divide  4178634  by  2,  by  3,  by  4,  by  5. 

97.  Divide  6783867  by  2,  by  3,  by  4,  by  5. 

98.  Divide  4067867  by  2,  by  3,  by  4,  by  5. 

99.  Divide  6703406  by  2,  by  3,  by  4,  by  5. 

100.  Divide  4678370  by  2,  by  3.  by  4,  by  5. 

101.  Divide  61011032  by  2,  by  3,  by  4,  by  5. 

102.  Divide  67834101  by  2,  by  3,  by  4,  by  5. 

103.  Divide  4186783  by  2,  by  3,  by  4,  by  5. 


DIVISION. 


107 


LESSON     XVII. 

TABLE. 

6  in     6,    OHO  3.         6  in  30,    5  times. 
6  in  12,    tWiC3.        6  in  36,     6  times. 
6  in  18,    3  times.      6  in  42,    7  times. 
6  in  2l,    4  times.      6  in  48,    8  times. 

6  in  54, 
6  in  60, 
6  in  66 
6  in  72, 

9  times. 
10  limes. 
11  times. 
12  times. 

Table  Exercise. 

1  is  0       6  ani  1  over. 
2  is  0  «  6  and  2  over. 
3  is  0  a  6  an*  3  over. 
4  is  0  +3  6  and  4  over. 
5  is  0       6  and  5  over 
etc. 

10—6;   11-7-6 
20  —  6  ;   21  -f-  6 
30  _  6  ;    81  -T-  6 
40  —  rt  ;   41-f-e 
50  —6  ;  51-7-6 
etc.            etc. 

;  12-6; 
;  22  -f-  6; 
;  32-*-6; 
;  42  +  6; 
;  52-6; 
etc. 

13  -f-  6  ;  etc. 
23  -j-  6;  etc. 
33  -i-  6  ;  etc. 
43  -T-  6  ;  etc. 
53  -v-  6  ;  etc. 
etc. 

BLACKBOARD    EXERCISES. 


(1)  • 

6)16  25  23  27  22  26  19  28  21  29  20  31  17 

(2) 

6)32  40  39  41  38  43  34  45  37  44  35  46  33 


LESSON    XVIII. 
MENTAL  EXERCISES.* 

1.  If  6  sheets  of  paper  make  a  copy-book,  how  many 
3>ooks  will  12  sheets  make? 

2.  If  one  yard  of  broadcloth  costs  6  dollars,  how  many 
yards  can  be  bought  for  30  dollars? 

3.  If  5  yards  of  broadcloth  costs  30  dollars,  what  will 
1  yard  cost? 

4.  If  a  man  travels  six  miles  in  one  hour,  how  many 

*  NOTE.— The  teacher  should  be  careful  and  require  the  appropriate  solution 
fcr  each  example 


108  DIVISION. 

hours  will  it  take  him  to  travel  12  miles?  72  miles?  54 
miles? 

5.  If  it  takes  a  man  7  hours  to  travel  42  miles,  how  far 
does  he  travel  in  one  hour? 

6.  If  it  take  1  man  6  hours  to  do  a  piece  of  work,  how 
long  will  it  take  6  men? 

7.  If  it  take  1  man  60  hours  to  do  a  piece  of  work, 
how  long  will  it  take  6  men? 

8.  If  1  man  can  dig  40  rods  of  ditch  in  *72  hours,  how 
long  will  it  take  6  men? 

9.  If  6  men  can  dig  42  rods  of  ditch  in  12  hours,  how 
many  rods  can  1  man  dig,  working  at  the  same  rate? 

10.  If  6  men  can  ^eat  a  tub  of  butter  weighing  54 
pounds,  in  36  days,  how  many  pounds  at  the  same  rate 
would  one  man  eat  in  the  same  time? 

11.  6  men  can  mow  36  acres  of  grass  in  6  days;  work- 
ing at  the  same  rate  how  many  acres  can  one  man  mow  ? 

12.  If  a  yard  of  ribbon  costs  6  cents,  how  many  yards 
can  be  bought  for  30  cents?  for  42  cents?  for  48  cents? 
for  18  cents? 

13.  If  a  pound  of  rice  costs  5  cents,  how  many  pounds 
can  be  purchased  for  60  cents?  for  85  cents?  for  35 
cents  ? 

14.  If  a  pound  of  lard  costs  6  cents  how  many  pounds 
can  be  purchased  for  12  cents?  for  54  cents?  for  66 
cents? 

15.  If  1  bushel  of  potatoes  cost  6  shillings,  how  many 
bushels  can  be  bought  for  72  shillings?  for  30  shillings? 
for  24  shillings?  for  18  shillings? 

16.  18  are  how  many  times  6?     3?     2?     8?     5?     4? 
1?     9?     7?     11?     12? 


DIVISION.  109 

LESSON  XIX. 
WRITTEN  EXERCISES. 

104.  Divide  41876834  by  3,  by  4,  by  5,  by  6, 

105.  Divide  37078642  by  3,  by  4,  by  5,  by  6. 

106.  Divide  40783742  by  3,  by  4,  by  5,  by  6. 

107.  Divide  4178683  by  3,  by  4,  by  5,  by  6. 

108.  Divide  3070800  by  3,  by  4,  by  5,  by  6. 

109.  Divide  41878G4  by  3,  by  4,  by  5,  by  6. 

110.  Divide  3718642  by  3,  by  4,  by  5,  by  6. 

111.  Divide  4078672  by  3,  by  4,  by  5,  by  6. 

112.  Divide  3704062  by  3,  by  4,  by  5,  by  6. 

113.  Divide  41307864  by  3,  by  4,  by  5,  by  6. 

114.  Divide  30710670  by  3,  by  4,  by  5,  by  6. 

115.  Divide  40701234  by  3,  by  4,  by  5,  by  6. 

LESSON  XX. 

116.  Divide  3070423  by  3,  by  4,  by  5,  by  6. 

117.  Divide  3407680  by  3,  by  4,  by  5,  by  6. 

118.  Divide  4107068  by  3,  by  4,  by  5,  by  6. 

119.  Divide  4187067  by  3,  by  4,  by  5,  by  6. 

120.  Divide  4087683  by  3,  by  4,  by  5,  by  6. 

121.  Divide  3496721  by  3,  by  4,  by  5,  by  6. 

122.  Divide  4257432  by  3,  by  4,  by  5,  by  6. 

123.  Divide  4132056  by  3,  by  4,  by  5,  by  6. 

124.  Divide  3247961  by  3,  by  4,  by  5,  by  6. 

125.  Divide  3798765  by  3,  by  4,  by  5,  by  6. 

126.  Divide  4207902  by  3,  by  4,  by  5,  by  6. 

127.  Divide  2142746  by  3,  by  4,  by  5,  by  6. 

128.  Divide  3579035  by  3?  by  4,  by  5,  by  6. 


11C 


DIVISION. 


7  in    7,  once. 

7  in  14,    twiC3. 
7  in  21,    3  times. 
7  in  28,    4  tim33. 

LESSON   XXI. 
TABLE. 

7  in  35,     5  times.  1 
7  in  42,     6  times.  | 
7  in  49,     7  times.  1 
7  in  56,     8  times.  | 

7 

7 
7 

7 

in  63,      9  times, 
in  70,    10  times, 
in  77,    11  times, 
in  84,    12  times. 

Table  Exercise. 

10-5-7; 

11 

-5-7;   12-4-7 

;  13 

-5-7; 

14 

_._ 

1; 

15 

•*-*; 

e^c. 

20-f-7; 

21 

-5-7;  22-?-7 

;  23 

-5-7; 

24 

_l_ 

?; 

25 

-s-f  ; 

dc. 

30-=-  7; 

31 

-4-7;  32-5-7 

;  33 

-4-7; 

34 

-4- 

*; 

35 

•7-f  ; 

</c. 

40-5-7; 

41 

-4-7;  42-f-7 

;  43 

—  7  • 

44 

_i_ 

*; 

45 

-5-7: 

c^c. 

50-5-7; 

51 

-4-7;  52-5-7 

;  53 

-f-7;' 

51 

-j_ 

7; 

55-4-7; 

c^c. 

etc. 

etc. 

e'c. 

etc. 

e^c. 

BLACKBOARD    EXERCISES. 


(1) 

7)23  31  29  32  30  33  25  36  27  34  26  37  24 


(2) 

7)38  45  43  48  44  47  40  46  42  50  41  51  39 


LESSON    XXII. 
MENTAL  EXERCISES. 

1.  If  7  sheets  of  paper  make  1  copy-book >  how  many 
books   can  be  made   from  49    sheets?    56    sheets?    70 
sheets? 

2.  If  7  boys  carry  63  pounds,  how  many  pounds  do 
one  of  the  boys  carry  ? 

3.  How  many  boys  will  it  take  to  carry  63  pounds,  if 
one  boy  can  carry  only  7  pounds  ? 


DIVISION.  Ill 

4.  If  there  are  7  sevenths  in  one  unit,  how  many  units 
in  14  sevenths? 

5.  If  I  have  77  sevenths  of  an  apple,  to  how  many 
boys  can  I  give  7  sevenths  of  an  apple  each  ? 

6.  If  I  have  21  ninths  of  an  orange,  to  how  many  girls 
can  I  give  7  ninths  of  an  orange  each  ? 

7.  There  are  7  sevenths  in  a  unit;  how  many  units  in 
72  sevenths? 

8.  One  man  can  do  a  certain  piece  of  work  in  35  days; 
how  many  days  will  7  men  require  to  perform  the  same 
work  ? 

8.  7  yards  of  cloth  cost  28  cents;  what  will   1   yard 
cost? 


LESSON   XXIII. 
WRITTEN"  EXERCISES. 

129.  Divide  40780641  by  4,  by  5,  by  6,  by  7. 

130.  Divide  3070346  by  4,  by  5,  by  6,  by  7. 

131.  Divide  30704261  by  4,  by  5,  by  6,  by  7. 

132.  Divide  4070673  by  4,  by  5,  by  6,  by  7. 

133.  Divide  3708641  by  4,  by  5,  by  6,  by  7. 

134.  Divide  30786043  by  4,  by  5,  by  6,  by  7. 

135.  Divide  4070834  by  4,  by  5,  by  6,  by  7. 

136.  Divide  30708642  by  4,  by  5,  by  6,  by  7. 

137.  Divide  89180034  by  4,  by  5,  by  6,  by  7. 

138.  Divide  60789019  by  4,  by  5,  by  6,  by  7. 

139.  Divide  39680723  by  4,  by  5,  by  6,  by  7. 

140.  Divide  37418679  by  4,  by  5,  by  6,  by  7. 
141    Divide  54786344  by  4,  by  5,  by  6,  by  7. 


112  DIVISION. 

LESSON   XXIV. 

142.  At  7   cents    apiece  how  many  pints  of  peanuts 
can  I  buy  for  56  cents  ?     For  1134  cents  ?     For  2268 
cents  ?     For  4536  cents  ? 

143.  At  5  shillings  a  pound  how  many  pounds  of  tea 
can  I  buy  for  65  shillings  ?     For   195  shillings  ?     For 
585  shillings?     For  1170  shillings? 

144.  At  6  cents  apiece  how  many  tops  can  I  buy  for 
72  cents  ?  For  504  cents  ?    For  1512  cents  ?    For  144  ? 

145.  I  have  648  dollars  with  which  to  buy  sheep  ;  how 
many  can  I  buy  at  2  dollars  a  head  ?  At  4  dollars  ?    At 
6  dollars  ?     At  3  dollars  ? 

146.  7  pieces  of  broadcloth  cost  448  dollars,  what  did 
one  of  the  pieces  cost?     What  did  two  of  them  cost? 
What  did  three  of  them  cost  ?     What  did  four  cost  ? 

147.  6  pieces  of  tape  contain   336  yards ;  what  does 
one  piece  contain  ?    2  contain  ?    3  contain  ?    4  contain  ? 

148.  Five   barrels    of  flour   are    worth    65    dollars; 
what  is  the  value  of  1  barrel?     Of  2  barrels?     Of  3 
barrels  ?     Of  4  barrels  ? 

149.  Seven  books  cost  399  cents;  what  did  1  book 
cost  ?  What  the  cost  of  2  books  ?  Of  3  books  ?  Of  4  books  ? 

150.  One  tub  of  butter    weighs   54  pounds;  at   the 
same  rate-what  will  3  tubs  weigh  ?     What  will  4  tubs 
weigh  ?     6  tubs  ?     7  tubs  ? 

151.  Six  houses  cost  4326  dollars;  what  did  1  cost? 
What  did  2  cost  ?  What  did  5  cost  ?  What  did  7  cost  ? 

152.  Six  stores  cost  8622  dollars ;  what  did  1  cost  ? 
What  did  2  cost  ?  What  did  3  cost  ?  What  did  4  cost  ? 

153.  If  one  pound  of  lard  is  worth  6  cents,  what  are  374 
pounds  worth  ?  867  pounds  ?  913  pounds  ?  713  pounds  ? 


DIVISION. 


113 


8  m    8,  once. 
8  in  16,  twice. 

8  in  24,    3  times. 
8  in  32,    4  times. 

10 -s- 8;  ll-r-8; 
20-*- 8;  21  -v- 8; 
30  -r-  8;  31 -j- 8; 
40  -l-  8  ;  41  -f-  8  ; 
50-8-8;  51-1-8; 
etc.  e'c. 


LESSON    XXV. 

TABLE. 

8  in  40,  5  times  I  8  in 
8  in  48,  6  times  |  8  in 
8  in  56,  7  times  8  in 
8  in  64,  8  times  |  8  in 

Table  JZxercisc. 
12^-8;  13  -v-  8;  14-*-  8 
22  -*-  8  ;  23  -v-  8  ;  24  -f-  8 
32  -r-  8;  33«-f-8;  34  -f-  8 
42  -r  8  ;  43  ~  8  ;  44  -r-  8 
52  +  8  ;  53  -f-  8  ;  54  ~  8 
e'c.  etc. 


72,  9  times. 

80,  10  times. 

88,  11  times. 

96,  12  times. 

;   15-J-8;  etc. 

;   25  -f-  8  ;  etc. 

;  35  —  8;  dc. 

;  45  ~-  8  ;  etc. 

;  65  •*-  8  ;  etc. 
etc. 


BLACKBOARD    EXERCISES.* 
(1) 

8)23  33  30  31  29  34  26  35  28  36  27 


8)38  46  45  47  44  49  41  51  43  50  42 


8)53  61  60  63  59  62  55  65  58  66  57 

(4) 
8)68  76  75  77  74  82  70  78  73  79  71 


LESSON   XXVI. 
MENTAL  EXERCISES. 

1.  At  8  cents  apiece,  how  many  cocoa-nuts  can  you 
buy  for  16  cents  ?  for  24  cents?   64  cents?  72  cents? 

*  NOTE.— The  teacher  should  not  fail  to  require  that  these  blackboard  exer- 
tises  bo  thoroughly  learned 


114  DIVISION. 

2.  If  8  pine-apples  cost  96  cents,  what  will  one  pine- 
apple cost  ? 

3.  If  you  have  48  cents  to  spend  for  grapes,  how  many 
bunches  can  you  buy  at  8  cents  a  bunch? 

4.  If  a  master-workman  have  56  dollars    to   divide 
equally  among  his  8  journeymen,  how  many  dollars  will 
each  journeyman  receive  ? 

5.  There  are   64  scholars    in   a  school;    how   many 
benches  will  they  occupy  if  8  sit  on  a  bench  ? 

6.  A   store-keeper   promised    to    divide    72    walnuts 
equally  among  8  children,  if  they  could  tell  him  how  many 
nuts  each  must  receive ;  what  should  be  the  reply  ? 

7.  In  a  certain  time  8  soldiers  can  eat  88  pounds  of 
bread ;  how  many  pounds,  at  that  rate,  can  one  soldier 
eat? 

8.  8  men  can  dig  96  bushels  of  potatoes  in  a  day ;  how 
many  bushels  can  one  man  dig? 

9.  During  a  certain  battle,  8  soldiers  fired  72  balls  at 
the  enemy ;  how  many  balls  did  one  soldier  fire  ? 

10.  Before  the  surrender  of  a  certain  fort,  96  cart- 
ridges were  equally  divided  among  8  soldiers  ;  and  as 
they   were  not  permitted  to  use   them,  how  many  had 
each  when  they  surrendered  ? 

11.  8  soldiers  received  16  pairs  of  stockings  to  be 
equally  divided  among  them ;  how  many  pairs  did  each 
receive  ? 

12.  In  8  quarts  there  is  1  peck;   how  many  pecks  in 
24  quarts?  in  40  quarts?  in  48  quarts?  64  quarts? 

13.  In  8  eighths  there  is  1  unit ;  how  many  units  in 
&0  eighths?  in  88  eighths?  in  8  eighths? 


•DIVISION.  115 

LESSON  XXVII. 
WRITTEN  EXERCISES. 

154.  Divide  407068342  by  5,  by"  6,  by  7,  by  8. 

155.  Divide  302416702  by  5,  by  6,  by  7,  by  8. 

156.  Divide  401000410  by  5,  by  6,  by  7,  by  8. 

157.  Divide  41070602  by  5,  by  6,  by  7,  by  8. 

158.  Divide  41307064  by  5,  by  6,  by  7,  by  8. 

159.  Divide  4034061  by  5,  by  6,  by  7,  by  8. 

160.  Divide  30708607  by  5,  by  6,  by  7,  by  8. 

161.  Divide  40706834  by  5,  by  6,  by  7,  by  8. 

162.  Divide  94196013  by  5,  by  6,  by  7,  by  8. 

163.  Divide  36709062  by  5,  by  6,  by  7,  by  8. 

164.  Divide  53021169  by  5,  by  6,  by  7,  by  8. 

165.  Divide  33410864  by  5,  by  6,  by  7,  by  8. 

166.  Divide  70370864  by  5,  by  g,  by  7,  by  8. 

LESSON    XXVIII. 

167.  Divide  4167086  by  5,  by  6,  by  7,  by  8. 

168.  Divide  4078603  by  5,  by  6,  by  7,  by  8. 

169.  Divide  3070642  by  5,  by  6,  by  7,  by  8. 

170.  Divide  3070412  by  5,  by  6,  by  7,  by  8. 

171.  Divide  34078602  by  5,  by  6,  by  7,  by  8. 

172.  Divide  30702162  by  5,  by  6,  by  7,  by  8. 

173.  Divide  4071862  by  5,  by  6,  by  7,  by  8. 

174.  Divide  41860304  by  5,  by  6,  by  7,  by  8. 

175.  Divide  83910670  by  5,  by  6,  by  7,  by  8. 

176.  Divide  30404012  by  5,  by  6,  by  7,  by  8. 

177.  Divide  35650456  by  5,  by  6,  by  7,  by  8. 

178.  Divide  73096781  by  5,  by  6,  by  7,  by  8. 


116 


DIVISION 


ESSOIST  xxix. 

TABLE. 

9  in 

9, 

once. 

9  in  45,    5  times. 

9 

in 

81, 

9 

times. 

9  in 

18 

twice 

9  in  54,    6  times. 

9 

in 

90 

10 

times. 

9  in 

27; 

3  times. 

9  in  63,    7  times. 

9 

in 

99, 

11 

times. 

9  in 

4  times. 

9  in  72,    8  times. 

9 

iu 

108 

12 

times. 

Table  Exercise. 

lO 

x  9 

;  11  x 

9; 

12  x  9;   13  x  9;  14  x 

9 

;  15 

x 

9; 

etc. 

10  -T-  9 

;  11  *~T" 

9; 

12-*-  9;  13  -T-  9;  14  -f-  9 

;   lo-r-9; 

etc. 

20 

x  9 

;   21   x 

9; 

22  x  9;   23  x  9;  24  x 

9 

;   25 

x 

9; 

etc. 

20-*- 9;  21-7-9;   22-7-9;  23  —  9;  24-7-9;  25  -f-  9  ;  etc. 
30  x  9 ;  31x9;  32  +  9 ;  33  x  9  ;  34  x  9 ;  25  x  9 ;  etc. 
etc.          etc.  etc.  etc.  etc.  etc. 

BLACKBOARD  EXERCISES. 
(1) 

9)42  50  49  52  48  51  44  53  47  55  46 


9)57  65  64  66  62  67  59  68  61  69  60 


(3) 

9)71  79  77  80  78  82  74  83  76  84  75 


(4) 
9)86  94  93  95  91  96  88  97  92  98  89 


LESSON    XXX. 
MENTAL  EXERCISES. 

1.  If  a  steamship  sails  9  miles  an  hour,  how  long  will 
tt  take  her  to  sail  36  miles?  9  miles?  18  miles? 


DIVISION.  117 

2.  A  steamship  can  sail  54  miles  in  9  hours ;    how 
many  miles  is  that  an  hour  ? 

3.  If  a  man  earn  9  dollars  in  a  week,  how  many  weeks 
must  he  work  to  earn  45  dollars?    108  dollars?    99  dol- 
lars? 

4.  If  a  boy  earn  36  dollars  in  9  weeks,  how  much 
does  he  earn  in  one  week  ? 

5.  You   wish  to   divide   54  dollars  equally  among  9 
men ;  how  much  should  each  man  receive  ? 

6.  If  you  have   72  dollars  which  you  wish  to  divide 
equally  among  some  poor  persons,  and  you  wish  to  give 
9   dollars  to   each  person,   how  many    can   share  your 
bounty  ? 

7.  A  soldier  who  was  wounded  in   a  certain   battle, 
in  9  months  received  from  the  soldiers'  fund  42  dollars ; 
how  much  was  that  a  month  ? 

8.  An  officer  who  was  wounded  during  the  Mexican 
war,  received  in  9  -weeks,  from  the   Government,   108 
dollars  ;  how  much  was  that  per  week  ? 

9.  If  you  have  90  lessons  to  get,  and  learn  only  9  les- 
sons a  week,  how  many  weeks  will  it  take  you  to  learn 
the  whole? 

10.  If  in  9  weeks  you  learn  99  lessons,  how  many  i? 
that  a  week  ? 

11.  If  9  yards  of  tape   cost   18   cents,  how  much  is 
that  a  yard  ? 

12.  If  9  yards  of  ribbon  cost  27  cents,  how  much  is 
that  a  yard  ? 

13.  At  9  cents  a  yard,  how  many  yards  of  muslin  can 
you  buy  for  63  cents?  for  54  cents?  for  45  cents? 


118  DIVISION. 

LESSON  XXXI. 
WRITTEN  EXEECISES, 

179.  Divide  41871864  by  6,  by  7,  by  8,  by  9. 

180.  Divide  4070304  by  6,  by  7,  by  8  by  9. 

181.  Divide  490706  by  6,  by  7,  by  8,  by  9. 

182.  Divide  30780467  by  6,  by  7,  by  8,  by  9. 

183.  Divide.  37080670  by  6,  by  7,  by  8,  by  9. 

184.  Divide  41830883  by  6,  by  7,  by  8,  by  9. 

185.  Divide  37086420  by  6,  by  7,  by  8,  by  9. 

186.  Divide  41708678  jy  6,  by  7,  by  8,  by  9. 

187.  Divide  53176083  by  6,  by  7,  by  8,  by  9. 

188.  Divide  15387560  by  6,  by  7,  by  8,  by  9. 

189.  Divide  36489615  by  6,  by  7,  by  8,  by  9. 

190.  Divide  63190358  by  6,  by  7,  by  8,  by  9. 

191.  Divide  98765432  by  6,  by  7,  by  8,  by  9. 

LESSON    XXXII. 

192.  Divide  38078642  by  6,  by  7,  by  8,  by  9. 

193.  Divide  40178067  by  6,  by  7,  by  8,  by  9. 
194  Divide  30708684  by  6,  by  7,  by  8,  by  9. 

195.  Divide  40370842  by  6,  by  7,  by  8,  by  9. 

196.  Divide  307086021  by  6,  by  7,  by  8,  by  9. 

197.  Divide  4012678  by  6,  by  7T  by  8,  by  9. 

198.  Divide  3070864  by  6,  by  7,  by  8,  by  9. 

199.  Divide  30418764  by  6,  by  7,  by  8,  by  9. 

200.  Divide  204785063  by  6,  by  7,  by  8,  by  & 

201.  Divide  380154732  by  6,  by  7,  by  8,  by  9. 
202-  Divide  123356789  by  6,  by  7,  by  8,  by  9. 
203.  Divide  987654821  by  6,  by  7,  by  8,  by  9. 


DIVISION. 


119 


LESSON    XXXIII. 

TABLE. 

10 

in 

o, 

0 

lime. 

11 

in 

o, 

0 

time. 

10 

in 

10 

1 

time. 

11 

in 

11 

1 

time. 

10 

in 

20 

2 

times. 

11 

in 

22, 

2 

times. 

10 

in 

30 

3 

times. 

11 

in 

33. 

3 

limes. 

10 

in 

40 

4 

tiuies. 

11 

in 

44, 

4 

times. 

10 

in 

50 

5 

times. 

11 

in 

55 

5 

times. 

10 

in 

60 

6 

times. 

11 

in 

66 

6 

times. 

10 

in 

70 

7 

times. 

11 

in 

77 

7 

times. 

10 

in 

80 

8 

times. 

11 

in 

88 

8 

times. 

10 

in 

90 

9 

times. 

11 

in 

99 

9 

times. 

10 
10 

in 
in 

100 
110 

10 
11 

times, 
times. 

11 
11 

in 
in 

110 
121 

10 
11 

times, 
times. 

10 

in 

120, 

12 

times.      |      1  1 

in 

132, 

12 

times. 

BLACKBOARD    EXERCISES. 


(1) 

10)10  109  54  119  65  116  32  112  76 


11)12  19  18  20  17  31  14  32  16  34  15 


11)36  45  42  43  41  46  38  47  40  49  39 


(4) 

11)60  68  67  69  65  70  62  71  64  72  63 


LESSON   XXXIV. 

MENTAL  EXERCISES, 

In  Multiplication  and  Division.* 

1.  If  1  yard  of  ribbon  costs  10  cents,  what  will  5  yards 
rost?  7  yards?  9  yards?  11  yards?  4  yards? 

•  NOTE  FOR  THE  TEACHER  —The  teacher  should  be  careful  to  require  th« 
Appropriate  solution  for  each  example. 


120  DIVISION. 

2.  If  one  yard  of  ribbon  costs  10  cents,  how  many  yards 
can  I  buy  for  50  cents?  for  80  cents?  for  120  cents? 

3.  If  7  yards  of  ribbon  cost  80  cents,  how  much  does 
one  yard  cost? 

4.  If  10  men  can  cut  20  cords  of  wood  in  2  days,  how 
many  cords  can  1  man  cut? 

5.  If  it  takes  10  men  2  days  to  cut  20  cords  of  wood, 
how  long  will  it  take  1  man  to  cut  the  same  amount? 

6.  If  it  takes  10  men  2  days  to  cut  20  cords  of  wood, 
how  many  men  will  it  require  to  cut  .it  in  1  day? 

7.  If  1 1  men  can  mow  55  acres  in  5  weeks,  how  much 
can  1  man  mow  in  5  weeks? 

8.  If  11  men  can  mow  55  acres  in  5  weeks,  how  long 
will  it  take  1  man  to  mow  it  ? 

9.  If  11  men  can  mow  55  acres  in  5  weeks,  how  many 
men  will  be  required  to  mow  it  in  1  week? 

10.  If  11  men  can  eat  66  pounds  of  flour  in  7  weeks, 
how  long  will  it  take  1  man  to  eat  it? 

11.  If  11  men  can  eat  66  pounds  of  flour  in  7  weeks, 
how  many  pounds  can  one  man  eat  in  the  same  time? 

12.  If  11  men  can  eat  66  pounds  of  flour  in  7  weeks, 
how  many  men  will  be  required  to  eat  it  in  1  week  ? 

13.  If  11  men  can  earn  88  dollars  in  9  weeks,  how 
much  can  1  man  earn  in  the  same  time? 

14.  If  11  men  can  earn  88  dollars  in  9  weeks,  how 
long  will  it  take  1  man  to  earn  the  same  amount? 

15.  If  11   men  can  earn  88  dollars  in  9  weeks,  how 
many  men  will  be  required  to  earn  it  in  1  week? 

1 6.  If  1  man  can  earn  8  dollars  in  a  week,  how  many 
Weeks  will  it  take  him  to  earn  88  dollars? 


DIVISION.  121 

LESSON    XXXV. 

WRITTEN  EXERCISES. 

204.  Divide  1678041864  by  11,  by  12,  by  13,  by  14, 

205.  Divide  18678S0142  by  11,  by  12,  by  13,  by  14. 

206.  Divide  37864134  by  12,  by  13,  by  14,  by  15. 

207.  Divide  40708646  by  12,  by  13,  by  14,  by  15. 

208.  Divide  40756413  by  13,  by  14,  by  15,  by  16. 

209.  Divide  30786412  by  14,  by  15,  by  16,  by  17. 

210.  Divide  9404603  by  15,  by  16,  by  17,  by  18. 

211.  Divide  7360421  by  16,  by  17,  by  18,  by  19. 

212.  Divide  5384671  by  17,  by  l6,  by  19,  by  20. 

213.  Divide  3468402  by  18,  by  19  by  20,  by  21. 

214.  Divide  4186302  by  19,  by  20,  by  21,  by  22. 

2 1 5.  Divide  4860960  by  20,  by  21,  by  22,  by  23. 

216.  Divide  4083786  by  21,  by  22,  by  23,  by  24. 

-      LESSON    XXXVII. 

217.  Divide  407864163  by  22,  by  23,  by  24,  by  25. 

218.  Divide  307864187  by  24,  by  25,  by  26,  by  27. 
21.9.  Divide  416780712  by  26,  by  27,  by  28,  by  29. 

220.  Divide  417083416  by  28,  by  29,  by  30,  by  31. 

221.  Divide  341816412  by  30,  by  31,  by  32,  by  33. 

222.  Divide  341783215  by  32,  by  33,  by  34,  by  35. 

223.  Divide  497826427  by  35,  by  36,  by  37,  by  38. 

224.  Divide  341864938  by  39,  by  40,  by  41,  by  42. 

225.  Divide  596782673  by  43,  by  44,  by  45,  by  46. 

226.  Divide  494187684  by  47,  by  48,  by  49,  by  50. 

227.  Divide  769689034  by  53,  by  55,  by  58,  by  60. 

228.  Divide  941856372  by  65,  by  68,  by  70,  by  75. 

229.  Divide  134670864  1  y  83,  by  88,  by  95,  by  98. 


122 


DIVISION. 


LESSON   XXXVII. 

TABLE. 

f2  in  12,  once. 
12  in  24,  twice. 

12  in  36,  3  times. 
12  in  48,  4  times. 

12  in  60,  5  times. 
12  in  72,  6  times. 
12  in  84,  7  times. 
12  in  96,  8  times. 

12  in  108,     9  times. 
12  in  120,  10  times. 
12  in  132,  11  times. 
12  m  144,  12  times. 

Table  Exercise. 

10  +  9;   11+9;  12+9;    13  +  9;   14+9;  etc. 
10  —  9;    11—9;    12  —  9;    13  —  9      14  —  9;  etc. 
10  x  9;  11  x  9;   12  x  9;    13   x  9     14  x  9  ;  etc. 
10  -*-  9  ;  11  -*-  9  ;    12  -=-  9  ;    13  -r-  9      14  -f-  9  ;  etc. 
20  +  9  ;  21  +  ^  ;   22  +  9  ;   23  +  9  ;   24  +  9  ;  etc. 
e'c.           etc.            etc.          etc.            e'c. 

BLACKBOARD    EXERCISES. 
(1) 

12)51  58  57  59  56  61  53  62  55  63  54 


12)65  73  74  71  70  75  67  76  69  77  68 


12)79  87  86 


85  89  81  90  83  91  82 


(*' 
12)93  101  100  99  103  95  104  98  105  97 


LESSON    XXXVIII. 

MENTAL  EXERCISES, 
In  Multiplication  and  Division. 

1.  If  12  horses  can  draw  24  tons  of  hay,  how  many 
tons  can  one  horse  draw  ? 


DIVISION.  123 

2.  If  1  horse  can  draw  2  tons  of"  hay,  how  many  tons 
can  1 2  horses  draw  ? 

3.  At  12  dollars  a  ton,  how  many  tons  of  hay  can  I 
buy  for  48  dollars  ? 

4.  If  I  have  96  dollars,  how  many  tons  of  hay  can  I 
buy  at  1 2  dollars  a  ton  ? 

5.  12  tons  of  hay  cost  144  dollars ;  how  much  did  one 
ton  cost? 

6.  If  1  ton  of  hay  costs  11  dollars,  how  much  will  "12 
tons  cost? 

7.  If  12  soldiers  ate  48  pounds  of  meat  in  12  meals, 
how  many  pounds  of  meat  did  1   of  the  soldiers  eat  in 
the  same  number  of  meals  ? 

8.  If  48  pounds  of  meat  will  last  12  soldiers  12  meals, 
how  many  meals  will  it  last  1  soldier? 

9.  If  12  soldiers  ate  48  pounds  of  meat  in  12  meals, 
how  many  pounds  would  they  eat  at  1  meal  ? 

10.  If  for  12  meals  12  soldiers  have  48  pounds  of  meat 
equally  divided  among  them,  how  many  pounds  will  each 
receive  ? 

11.  Sixty  blankets  were  distributed  equally  among  12 
Indians  ;  how  many  blankets  did  each  Indian  receive  ? 

12.  If  a  shjp  sail  12  miles  an  hour,  how  many  miles 
will  she  sail  in  1 1  hours  ?  9  hours  ?  7  hours  ? 

13.  If  a  ship  sail  12  miles  an  hour,  how  many  hours 
will  it  take  her  to  sail  84  miles?    48  miles?    60  miles? 
86  miles?   132  miles? 

14.  If  1  cord  of  wood  is  worth  12  shillings,  how  many 
shillings  will  7  cords  be  worth  ?  6  cords  ?  3  cords  ? 

15.  3  times  4  are  how  many  times  2 ?  6?  9?  4?  3?  8r 


124 


DIVISION. 


LESSON    XXXIX. 

WRITTEN  EXERCISES. 

230.  Divide  40708302  by  99,  by  109,  by  209,  by  211. 

231.  Divide  3078643  by  200,  by  207,  by  217,  by  297. 
L32.  Divide  4070864  by  301,  by  308,  by  329,  by  3890 

233.  Divide  30460780  by  491,  by  437,  by  463,  by  478. 

234.  Divide  4070340  by  500,  by  538,  by  507,  by  533. 

235.  Divide  3087864  by  660,  by  675,  by  611,  by  625. 

236.  Divide  3498347  by  721,  by  637,  by  686,  by  675. 

237.  Divide  3678416  by  829,  by  808,  by  897,  by  857. 

238.  Divide  4189674  by  960,  by  950,  by  968,  by  940. 

239.  Divide  3783641  by  864,  by  784,  by  683,  by  404. 

240.  Divide  6467834  by  913,  by  683,  by  407,  by  306. 

241.  Divide  1867834  by  914,  by  867,  by  537,  by  409. 

242.  Divide  3868347  by  630,  by  807,  by  570,  by  308. 

LESSON  XL. 

243.  Divide  4070861  by  86,  by  68,  by  100,  by  1001. 

244.  Divide  3070842  by  10,  by  20,  by  30,  by  1000. 

245.  Divide  4030702  by  40,  by  50,  by  60,  by  4000. 

246.  Divide  406703  by  25,  by  70,  by  80,  by  5005. 

247.  Divide  3070864  by  30,  by  90,  by  76,  by  6060. 

248.  Divide  4070041  by  43,  by  67,  by  83,  by  7007. 

249.  Divide  467834  by  39,  by  67,  by  94,' by  8080. 

250.  Divide  738416  by  37,  by  44,  by  67,  by  5099. 

251.  Divide  874034  by  69,  by  12,  by  29,  by  3907. 

252.  Divide  537068  by  76,  by  87,  by  95,  by  -8406. 

253.  Divide  708064  by  99,  by  88,  by  77,  by  9009. 

254.  Divide  307806  by  66,  by  55,  by  44,  by  9876. 


MISCELLANEOUS.  125 

LESSON    XLI. 
f  MISCELLANEOUS  MENTAL  EXERCISES. 

1.  There  were  9  apples  on  the  table,  and  Charles  look 
3  of  them  ;  how  many  remained  ? 

2.  If  1   apple  is  worth  2   cents,  how  much  will  1 2 
apples  be  worth  ?  7  apples  ?  5  apples  ? 

3.  Charles  had  7  nuts,  and  his  sister  gave  him  8  more , 
how  many  had  he  then  ? 

4.  Marcus  bought  a  slate  for  19  cents,  and  then  sold  it 
for  8  cents  less  than  he  gave  for  it ;  how  much  did  he 
receive  for  it  ? 

5.  Henry  bought  a  sled  for  23  cents,  ar.d  then  sold  it 
for  9  cents  more  than  he  gave  for  it;  how  much  did  he 
receive  for  it  ? 

6.  If  9  sheep  are  worth  108  dollars,  how  much  is  one 
of  the  sheep  worth  ? 

7.  How  much  will  11  sheep  cost,  at  5  dollars  a  head? 

8.  If  I  have  37  sheep  and  lose  9,  how  many  will  ] 
have  left  ? 

9.  A  boy  had  7  cents,  and  his  brother  gave  him  9 
more  ;  how  many  had  he  then  ? 

10.  A  boy  bought  a  slate  for  10  cents;  he  gave  the 
clerk  a  25  cent  postage-bill ;  how  much  change  should  he 
receive  in  return  ? 

11.  What  will  7  pounds  of  raisins  cost  at  22  cents  a 
pound?  at  9  cents?  at  1 1  cents?  at  10  cents? 

12.  7  hats  cost  28  dollars;  what  did  one  of  the  hata 
cost? 

13.  1  had  27  dollars,  and  gave  9  dollars  to  my  sister  j 
how  many  dollars  had  I  left  ? 


126  MISCELLANEOUS. 

LESSON    XLII. 

1.  A  boy  had  27  marbles ;  in  playing  he  lost  all  but 
9 ;  how  many  did  he  lose  ? 

2.  How  many  oranges  at  6  cents  apiece  can  you  buy 
for  42  cents  ?  for  54  cents?  for  60  cents?  for  72  cents? 

3.  A  farmer  pays   28  dollars  for  7  sheep ;  how  much 
is  that  apiece  ? 

4.  A  trader  wishes  to  pack  64  hats  in  boxes,  and  can 
put  but  8  hats  in  a  box;  how  many  boxes  does  he  need? 

5.  If  a  man  can  build  7  rods  of  fence  in  a  day,  how 
long  will  it  take  him  to  build  77  rods  ? 

6.  What  will  9  pounds  of  sugar  cost,  at  9  cents  a 
pound  ? 

7.  What  is  the  cost  of  12  pounds  of  tea,  at  12  shil- 
lings a  pound  ? 

8.  John  bought  9  pencils  at  2  cents  apiece ;  how  much 
did  they  cost  him  ? 

9.  I  have  a  -string  27  feet  long ;  how  much  will  remain 
after  I  cutoff  >*  feet? 

10.  There  are  16  cows  in  the  pasture ;  John  drove  out 
6  ;  how  many  remained  ? 

11.  Charles  picked  13  bushels  of  apples,  and  George 
picked  as  many  lacking  5  bushels ;  how  many  did  George 
pick  ? 

12.  If  7   pigs   cost   63   dollars,  how  much  was  that 
apiece  ? 

13.  If  9  calves  cost  72  dollars,  how  much  was  that 
apiece  ? 

14.  How  much  will  7  coats  cost  at  12  dollars  apiece? 


MISCELLANEOUS.  127 

LESSOK    XLI. 

MISCELLANEOUS  WRITTEN  EXERCISES. 
.  255.  A  man  had  5671  dollars ;  he  paid  to  one  man 
1480  dollars,  how  much  had  he  left  ?  He  paid  to  an- 
other 378  dollars;  how  much  had  he  left?  He  lo^t 
576  dollars;  how  much  had  he  left?  He  had  1000 
dollars  stolen  ;  how  much  finally  remained  ? 

256.  What  will   347    oranges  cost  at  2  cents  each  ? 
At  6  cents  each  ?     At  9  cents  each  ?     At  8  cents  eacli  ? 

257.  What  will  be  the  cost  of  35  sheep  at  7  dollars 
each  ?     27  cows  at  26  dollars  each ;  57  horses  at  137 
dollars  each  ? 

258.  Samuel  shot  two  arrows  in  the  same  direction, 
one  went   387  feet,  the  other  433   feet ;  how  far  were 
they  apart  ? 

259.  He  asked  a  little  boy  to  get  them;  how  much 
farther  must  he  walk  to  bring  the  one  than  the  other? 

260.  The  bridge  is  116  rods  up  the  road  from  the 
school-house,  the  oak  tree  is  250  rods  down  the  road; 
how  far  is  the  bridge  from  the  oak  tree  ? 

261.  The  village   mill  is  680  rods  from  the  school- 
house,    two  boys  walked  there  and    back ;  how   many 
rods  did  they  walk  ? 

262.  A  merchant   bought  347  yards  of  cloth  at  one 
time,   673    yards   at  another  time,    and  467   yards    at 
another ;  how  much  did  he  buy  in  all  ? 

263.  If  I  travel  137  miles  on  one  day,  and  237  miles 
on  the  next  day,  how  far  will  I  travel  in  all  ?. 

264.  I  was  374  miles  from   home,  on  the  next  day  I 
was  570  miles  from  home ;  which  way  and  how  far  did 
I  travel ? 


128  MISCELLANEOUS- 

265.  A  little  boy  was  39  rods  from  the  school-house, 
he  walked  15  rods  farther ;  how  far  was  he  then  from 
the  school-house  ? 

266.  A  large  boy  threw  a  stone  to  the  oak  tree  which 
was  632  feet  up  the  road     he  then  walked  to  the  mill, 
which  was  513  feet  down   the  road;  how  far  was  the 
mill  from  the  oak  tree  ? 

267.  A  man  had  two  notes  due  him,  one  for   1374 
dollars,  the  other  for  347  dollars;  how  much  was  due 
him  in  all  ? 

268.  A  piece  of  tape  contained  38  yards ;  John  cut 
off  13  yards ;  how  many  yards  remained  ? 

269.  A  man  bought  a  house  and  sold  it  for  3741  dol- 
lars, which  was  341  dollars  less  than  he  gave  for  it ;  how 
much  did  he  give  for  it  ? 

270.  Samuel  gave  371  cents  for  some  nuts,  which  is 
211  cents  less  than  they  are  worth;   how  much  are  they 
worth  ? 

271.  Samuel  gave  371  cents  for  some  melons,  which 
is  211  cents  more   than  they  are  worth;  what  are  they 
worth  ? 

272.  A  man  bought  a  house  for   1372  dollars,  which 
is  376  dollars  more  than  it  is  worth ;  what  is  it  worth  ? 

273.  A  man  bought  a  house  for  1372  dollars,  which 
is   376   dollars   less    than    it   is    worth ;    what    is    it 
worth  ? 

274.  I  bought  some  sheep  for  483  dollars,  and  some 
cows  for  473  dollars  ;  how  much  more  did  the  sheep  cost 
than  the  cows  ? 

275.  A  man  bought  396  bushels  of  corn  ;  all  but  125 
bushels  were  sunk  in  a  boat ;  how  much  was  saved  ? 


MISCELLANEOUS.  120 

276.  Thomas  Jones  bought  576  bushels  of  wheat;  his 
brother  bought  as  many  bushels,  lacking  188  bushels ; 
how  many  bushels  did  his  brother  buy  ? 

277.  What  will  164  pairs  of  boots  cost  at  5  dollars  a 
pair  ? 

278.  What  is  the  value  each  of  the  following  articles  : 
12  pounds  of  cheese  at  16  cents  a  pound  ;  9  pounds  of 
rice  at  7  cents  a  pound  ;  12  pounds  of  raisins  at  13  cents 
a  pound  ? 

279.  What  is  the  value  of  each  of  the  following  arti- 
cles :   13  gallons  of  vinegar  at  13   cents  a  gallon ;  27 
gallons  of  molasses  at  36  cents  a  gallon  ;  25  gallons  of 
oil  at  37  cents  a  gallon  ? 

280.  There  are  40  lines  on  one  page,  how  many  lines 
in  a  book  of  375  pages  ? 

281.  Five  hundred   and  sixty-eight  cents  is  the  cost 
of  four  books  ;  what  is  the  cost  of  one  of  the  books  ? 

282.  Five  boats  carry  3765  pounds     how  much  does 
one  of  the  boats  carry  ? 

283.  If  one  boat  can   carry  3765  pounds,  how  many 
pounds  can  five  boats  of  the  same  size  carry  ? 

284.  378  pounds  of  sugar  cost  3024  cents;  how  much 
is  that  a  pound  ? 

285.  496  bushels  of  wheat  are  worth  992  dollars;  how 
much  is  that  a  bushel  ? 

286.  5786  oranges  cost  28930  cents ;  how  much   is 
that  apiece? 

287.  2692   cents   were   paid   for  673  peaches;    how 
much  is  that  apiece  ? 

288.  In  one  pound  there  are  16  ounces;   how  many 
ounces  in  437  pounds  ? 


130 


FEDERAL   MONEY. 


SECTION    VI. 

LESSON   L 
FEDERAL  MONEY. 

Federal  Money  is  the  currency  of  the  United 
States. 

The  Denominations  are  eagles,  dollars,  dimes, 
cents,  and  mills. 

The  Coins  are  the  eagle,  half-eagle,  quarter- 
e,agle,  dollar,  half-dollar,  quarter-dollar,  dime,  hall- 
dime,  three-cent  piece,  two-cent  piece,  and  cent. 


TABLE. 

10  mills  (in.)  make  1  cent. 

10  cents          make  1  dime. 

10  dimes         make  1  dollar. 

10  dollars 


ct. 
d. 


make     1     eagle. 


Gold. 


Gold. 


Gold. 


FEDERAL    MONEY.  131 

LESSON   II. 
MENTAL  EXERCISES. 

1.  How  many  mills  in  5  cents  ? 

SOLUTION. — Since  in  1  cent  there  are  10  mills,  in  5  cents  there  are 
5  times  10  mills,  which  are  50  mills. 

Therefore,  in  5  cents  there  are  50  mills. 

2.  How  many  dimes  in  8  dollars?    in  6  dollars?  in   3 
dollars? 

3.  How  many  dollars  in  8  eagles?  in  6  eagles?  in  5  ea- 
gles? 

4.  How  many  cents  in  3  dimes?  in  6  dimes?  in  3  dimes? 

5.  If  1  pair  of  gloves  costs  10  dimes,  how  ma&y  dimes 
will  7  pairs  cost?  5  pairs?  9  pairs?  8  pairs? 

6.  How  many  cents  in  80  mills? 

SOLUTION. — Since  in  10  mills  there  is  1  cent,  in  80  mills  there  aro 
as  many  cents  as  10  mills  are  contained  tinaes  in  sO  miil&,  which  are  8 
times. 

Therefore,  in  80  mills  there  are  8  cents. 

7.  How  many  dimes  in  70  cont»?  in  90  cents? 

8.  How  many  dollars  in  90  dimes?  in  70  dimes? 

9.  How  many  eagles  in  70  dollars  ?  in  30  dollars  ? 

10.  What  will  7  apples  cost  at  3  cents  apiece?    at   0 
cents  ?  at  8  cents  ? 

11.  How  many  cents  will  4  yards  of  cloth  cost  at  3 
dimes  a  yard  ? 

12.  What  will  4  handkerchiefs  cost  at  7  dimes  apiece. 

13.  How  many  cents  in  3  eagles?  2  dollars?  in  4  dol- 
lars? 2  dimes? 


132 


ENGLISH    MONEY. 


LESSON   III. 
ENGLISH   MONEY. 

English  Money  is  the  currency  of  Great  Britain. 
The    Denominations    are    pounds,    shillings, 
pence,  and  farthings. 

The  Coins  are  the  sovereign,  half-sovereign,  shil- 
ling, six-pence,  penny,  half-penny,  and  farthing. 


TABLE. 


4  farthings  (far.)  make 

12  pence                 make     j.  oumujg. 

make-!1  P°und<?r        I 

(  sovereign,     j 


20  shillings 

21  shillings 


1  penny. 
1  shilling. 


make 


sovereign. 
1  guinea. 


d. 

s. 

£. 


guin. 


r.— Copper— 5  nulls.  Sov.— Gold— $4  84.  Silver— 18  cte. 

jiote. — The  franc  is  a  French  C3in. 


ENGLISH   MONEY. 
LESSON   IV. 


133 


Copper— 1  cent. 


HalfSov.— Gold— $2  42. 


MENTAL  EXERCISES. 

1.  How  many  farthings  in  4  d.  ? 

SOLUTION.— Since  there  are  4  farthings  in  1  penny,  in  4  pence  there 
are  4  times  4  farthings,  which  are  16  farthings. 
Therefore,  in  4  pence  there  are  16  farthings. 

2.  How  many  farthings  in  9  pence  ?  in  8  d.  ?  in  12  d.  ? 

3.  How  many  shillings  in  3  pounds  ?  in2«£?  in  4  £  ? 

4.  How  many  shillings  in  2  guineas?  in  3  guin. ?  in  4 
guin. ? 

5.  How  many  shillings  in  3  sovereigns  ?  in  6  sov.  ? 

6.  How  many  shillings  in  48  pence  ? 

SOLUTION.— Since  in  12  pence  there  is  1  shilling,  in  48  pence  there 
are  as  many  shillings  as  12  pence  are  contained  times  in  48  pence, 
which  are  4  times. 

Therefore,  in  48  pence  there  are  4  shillings. 

7.  How  many  pence  in  48  farthings  ?  in  44  farthings  ? 

8.  How  many  shillings  in  36  pence  ?  in  60  pence  ? 

9.  How  many  pounds  in  80  shillings  ?  in  40  shillings  ? 

10.  How  many  guineas  in  42  shillings  ?  in  63  s.  ? 

11.  Change  3  shillings  to  pence.  [ 

12.  Change  108  pence  to  shillings. 

13.  Change  3  guineas  to  shillings. 


134 


AVOIRDUPOIS   WEIGHT. 


LESSON   V. 
AVOIRDUPOIS  WEIGHT. 


Avoirdupois  Weight  is  used  for  all  ordinary 
purposes. 

The  Denominations  are  tons,  hundred-weights, 
quarters,  pounds,  ounces,  and  drams. 


TABLE. 

16  drams  (dr.)  make        1     ounce.  oz. 

16  ounces  make  1     pound,  Ib. 

25  pounds  make  1     quarter.  qr. 

100  pounds  or    {        ^        ,  j  hundred  )  . 

4  quarters       j  r  (  weight.    \ 

20  hundred  weight  make  1     ton.  T. 

TABLE   OP   THE    LONG   TON* 

28     pounds  (Ibs.)        make     1     quarter  marked     qr. 

4     quarters  make     1     hundred  weight      "        cwt. 

20    hundred  weight    make     1    gross  ton  **      G.  T. 


7000  gr. 

*  Note. — The  exact  weight  of  an  Avoirdupois  dram  is  27-j 
grains. 


Troy 


AVOIRDUPOIS    WEIGHT. 
LESSON  VI. 


135 


1  firkin. 


1  barrel 


1  barreL 


1  bushel. 


1  barreL 


1  bushel. 


1  bushel. 


1  bushel. 


136  AVOIRDUPOIS   WEIGHT. 

LESSON    VII. 
MENTAL  EXERCISES. 

1.  How  many  drams  in  2  ounces  ?  in  3  oz.  ? 

2.  How  many  ounces  in  2  pounds  ?  in  3  Ibs.  ? 

3.  How  many  pounds  in  4  quarters  or  1  cwt  ? 

4.  How  many  quarters  in  8  hundred  weight  ? 

5.  How  many  hundred  weight  in  2  tons  ? 

6.  How  many  ounces  in  32  drams? 

7.  In  48  ounces  how  many  pounds  ? 

8.  In  40  quarters  how  many  hundred  weight? 

9.  In  60  hundred  weight  how  many  tons  ? 

10.  In  50  pounds  how  many  quarters  ? 

11.  In  80  ounces  how  many  pounds? 

12.  How  many  quarters  in  100  pounds  ? 

13.  How  many  ounces  in  80  drams? 

14.  How  many  tons  in  80  hundred  weight  ? 

15.  How  many  ounces  in  6  pounds  ? 

16.  What  will  2   ounces  of  cinnamon  cost  at  8  cents  an 
ounce  ? 

17.  What  will  3  pounds  of  rice  cost  at  12  cents  a  pound  ? 

18.  What  will  3   hundred  weight  of  hay  cost  at  3  dollars 
per  hundred  weight  ? 

19.  At  8  cents  an  ounce,  how  many  ounces  of  pepper  can 
I  buy  for  40  cents? 

20.  At  12  cents  a  pound,  how  many  pounds  of  sugar  can 
be  bought  for  84  cents  ? 


TROY    WEIGHT.  137 

LESSON   VIII. 
TROY    WEIGHT. 

Troy  Weight  is  used  in  weighing  gold,  silver 
and  jewels,  and  in  philosophical  experiments. 

The  Denominations  are  pounds,  ounces,  penny- 
weights, and  grains. 

TABLE. 

24  grains      (gr.)     make  1  pennyweight,    pwt. 
20  pennyweights    make  1  ounce.  oz. 

12  ounces  make  1  pound.  Ib. 


24  grs.  480  grs.  5760  grs. 

Note. — 3£  grains  make  a  carat,  Diamond  weight. 
MENTAL  EXERCISES. 

1.  How  many  grains  in  2  pennyweights? 

2.  In  72  grains  how  many  penny  weights  ? 

3.  How  many  pennyweights  in  3  ounces? 

4.  In  80  pennyweights  how  many  ounces? 

5.  How  many  ounces  in  9  pounds? 

6.  How  many  pounds  in  36  ounces? 

V.  How  many  grains  in  T  pennyweights? 


138 


APOTHECARIES'  WEIGHT. 


LESSON   IX. 
APOTHECARIES'  WEIGHT. 


Apothecaries'  Weight  is  used  by  physicians  in 
compounding  medicines ;  but  medicines  are  bought 
and  sold  by  avoirdupois  weight. 

The  Denominations  are  pounds,  ounces,  drams, 
scruples,  and  grains. 


TABLE. 


20  grains  (gr.)  make  1  scruple. 

3  scruples        make  1  dram. 

8  drams           make  1  ounce. 

12  ounces          make  1  pound. 


sc.  or  3. 
dr.  or  3. 
oz.  or  5 . 
Ib.  or  ft. 


20  grs. 


60  grs. 


480  grs. 


57CO  grs. 


LESSON   X. 
MENTAL  EXERCISES. 

1.  How  many  grains  in  3  scruples?  in  4  scruples? 

2.  How  many  scruples  in  11  drams?  in  9  drams? 

3.  How  many  scruples  in  80  grains  ?  in  40  grains  ? 

4.  How  many  drams  in  27  scruples?  in  24  B? 

5.  How  many  ounces  in  24  drams?  in  16  3  ? 

6.  How  many  ounces  in  12  pounds?  in  10  pounds? 
V.  How  many  ounces  in  96  drams  ?  in  88  3  ? 

8.  In  7  ounces  how  many  drams? 


LIN  EAT.  ?,:::AsrttE. 


139 


WILLIAM. — Father,  how  far  is  a  mile? 

FATHER. — To  make  a  foot,  cut  12  sticks  each  an  inch 
long,  and  place  tliem  in  a  row. 

To  make  a  yard,  cut  a  string  three  times  as  long  as  your 
row  of  sticks. 

To  make  a  rod,  cut  a  pole  like  the  one  in  your  hand, 
five  and  a-half  times  the  length  of  the  string. 

Forty  times  the  length  of  the  pole  is  the  length  of  t'.c 
door-yard  fence  yonder,  or  one  furlong. 

Eight  times  the  length  of  the  fence,  is  the  distance  from 
the  guide-post  to  the  rail-road  hridge,  or  one  mile. 

"We  have  just  time  to  walk  down  to  the  bridge  and 
back  before  dinner ;  how  far  will  that  be  ? 


140 


LINEAR   MEASURE. 


LESSON   XI. 

LINEAR    MEASURE. 
Linear  Measure  is  used  for  measuring  distance. 

The  Denominations  are  miles,  furlongs,  rods, 
yards,  feet,  and  inches. 

TABLE. 


12 

inches  (in.) 

make 

1 

foot. 

ft. 

3 

feet 

make 

1 

yard. 

7d- 

H 
11 

L6J 

yards  or      ) 
half-yards,  >- 
feet              ) 

make 

! 

l  < 

1 

Jrod,           ) 
perch,  or  V 
'  pole.          ) 

rd. 

40 

rods 

make 

1 

furlong. 

fur. 

8 

furlongs 

make 

1 

mile. 

mi. 

TABU6   OF    MISCELLANEOUS    LINEAR    MEASURE. 


4  inches 

9  inches 
3  feet 

6  feet 


(  used  in  measuring  the 
make  1  hand    <  height  of  horses  direct- 
{ ly  over  the  fore-feet. 

make  1  span. 

make  1  pace,  or  step.    , 


'  i  in  i  i 


1  inch. 


CLOTH    MEASURE.  141 

LESSON   XII. 
CLOTH    MEASURE. 

Cloth  Measure  is  used  for  measuring  goods 
sold  by  the  yard,  as  cloth,  lace,  ribbon,  &c.  . 

The  Denominations  are  yards,  quarters,  inches, 
and  nails. 

TABLE. 

2j  inches  (in.)  make     1     nail.  na. 


4  quarters  make     1     yard.  yd. 

LESSON   XIII. 
MENTAL  EXERCISES. 

1.  How  many  .inches  in  3  feet?  in  6  feet? 

2.  How  many  feet  in  8  yards?  in  12  yards? 

3.  How  many  /laZ/'-yards  in  22  yards  ? 

4.  Row  m.,ny  rods  in  44  halt- yards? 

5.  How  many  rods  in  83  yards?  * 

6.  How  many  rods  in  44  yards  ? 

7.  How  many  furlongs  in  5  miles?  in  9  miles? 

8.  How  many  nails  in  3  quarters? 

9.  How  many  quarters  in  7  yards  ? 

10.  H«w  many  nails  in  3  quarters  and  2  nails? 

11.  How  many  yards  in  44  quarters  ? 

12.  How  many  quarters  in  24  nails? 

13.  How  many  inches  in  1  yard  ? 

14.  How  many  yards  in  36  inches? 

15.  How  many  yards  in  48  quarters? 

*  Change  the  yards  to  /m^-yards,  then  the  Aa//"-ynrds  to  rod* 


142 


SQUARE    MEASURE. 


FATHER. — Charles,  if  yon  wish  to  know  how  much  land 
my  farm  contains,  cut  144  pieces  of  pnper  one  inch  square, 
and  pLce  them  in  a  large  square ;  this  is  called  a  square 
foot. 

To  make  a  square  yard,  place  9  square  feet  in  a  large 
square. 

To  make  a  piece  of  land  the  s'ze  of  the  flower-bed  in 
the  door-yard,  it  will  require  80]-  square  yards,  which  is 
called  a  square  rod. 

Forty  square  rods  is  just  one  m?J,  or  a  quarter  of  an 
acre  of  land,  and  is  the  size  of  the  lot  across  the  road  in 
which  you  see  the  sheep. 

The  lot  in  which  you  see  the  man  plowing,  contains  4 
roods  of  land,  and  is  called  an  acre. 

640  acres  make  one  square  mile  of  land,  which  is  the 
size  of  my  farm. 

"We  will  rMe  over  it  after  you  have  recited  the  table. 


SQUARE   MEASURE.  143 

LESSON   XIV. 
SQUARE    MEASURE. 

Square  Measure  is  used  in  computing  the  area 
of  surfaces. 

The  Denominations  are  acres,  roods,  square 
rods,  square  yards,  square  feet,  and  square  inches. 

TABLE. 

144     square  inches  (in.)  make  1  square  foot.    sq.  ft. 

9     square  feet              make  1  square  yard.  sq.  yd. 

30£  square  yards  or  )        i  -,             -, 

121     qr.  square  yards  \  make  l  81uare  rod'    «!•  rd' 

40    square  rods  make  1  j  ™o<*  or  1ual"  1  R. 

(  ter  01  an  acre,  j 

,  j  quarter-acres  or  } 

[      roods,  or          >  make  1     acre.  A. 

160     square  rods 


LESSON    XV. 

MENTAL  EXERCISES. 

1.  In  3  square  yards  how  many  square  feet? 

2.  How  many  roods  in  9  acres  ?  in  7  acres  ? 

3.  How  many  ncres  in  16  roods?  in  48  roods? 

4.  How  many  roods  in  80  square  rods  ? 

5.  How  many  roods  in  5  acres? 

6.  How  many  acres  in  16  quarter  acres? 


144 


CUBIC   MEASURE. 


LESSON  XVI. 
CUBIC    MEASURE. 

Cubic  Measure  is  used  to  estimate  the  contents 
of  solids. 

The  Denominations  are  cords,  tons,  cubic  yards, 
cubic  feet,  and  cubic  inches. 

TABLE. 

1728  cubic  inches  (cu.  in.)  make  1  cubic  foot.    cu.  ft. 
27  cubic  feet  make  1  cubic  yard.  cu.  yd. 

16  cubic  feet  make  1  cord  foot.     cd.  ft. 

42  cubic  feet  make  1  ton,  shipping,  t.  s. 

8  cord  feet  or  ) 
128  cubic  feet      ( 


make  1  cord  of  wood.  cd. 


Cubic  foot.  Cubic  yard. 

Note. — 24|  cubic  feet  make  1  perch  of  stone  or  masonry. 


C::BIO  MEASURE. 


8  FT  LONG 


Cord  of  wood. 


LESSON    XVII. 
MENTAL  EXERCIiTES. 

1.  How  many  cord  feet  in  2  cords?  in  5  cords? 

2.  In  32  cabic  fret  how  many  cord  fe  t  ? 

3.  How  many  cubic  feet  in  2  cubic  yards? 
i.  How  many  cubrc  feet  in  0  cubic  yards? 

5.  How  many  feet  in  3  cor;l  feetf 

6.  What  will  3  cords  of  wood  cost  at  $5  a  cord? 

7.  What  will  3  cubic  feet  of  granite  cost  at  12  cents  per 
tabic  foot  ? 

8.  How  many  inches  in  7  feet  ?  in  G  feet  ? 

9.  How  many  feet  in  9  yards  ?  in  7  yards  ? 

10.  How  many  Jialj '-yards  in  8  yards  ? 

• 

11.  How  many  yards  in  88  half-yards? 

12.  How  many  furlongs  in  8  miles?  in  7  miles? 

13.  What  is  the  difference  between  a  foot  in  length  and  a 
eqnare  foot?  a  square  fo:  t  and  a  cubic  foot? 

10 


146 


WINE   MEASURE. 


LESSON    XVIII. 
WINE    MEASURE. 


"Wine  Measure  is  used  in  measuring  liquids. 
The  Denominations  are  hogsheads,  barrels,  gal- 
lons, quarts,  pints,  and  gills. 


TABLE. 


4 

gills  (gi.) 

make 

1 

pint. 

pt. 

2 

pints 

make 

1 

quart. 

qt. 

4 

quarts 

make 

1 

gallon. 

gaL 

IU 

13 

fallons  01 
alf  gals. 

i 

make 

1 

barrel. 

bbl. 

2     barrels  or)  ke     h       heai 

63     gallons       [ 


hhd. 


I  "barrel. 


1  hogshead. 


WINE   MEASURE. 


-147 


LESSON   XIX. 
MENTAL  EXERCISES. 

1.  How  many  gills  in  6  pints?  in  8  pints? 

2.  How  many  pts.  in  12  quarts?  in  8  qts.  ? 

3.  How  many  quarts  in  11  gallons? 

4.  In  24  pints  how  many  quarts  ? 

5.  In  16  quarts  how  many  gallons? 

6.  In  24  gills  how  many  pints  ? 

LESSON   XX. 
DRY    MEASURE. 

Dry  Measure  is  used  in  measuring  vegetables 
fcnd  articles  not  fluid. 

The  Denominations  are  bushels,  pecks,  quarts/ 
and  pints. 

TABLE. 


2     pints  (pt.)  make     1     quart. 
8     quarts         make     1     peck. 
4     pecks 


make     1 


Note. — 36  bushels  make  a  chaldron. 

LESSON   xxi. 
MENTAL  EXERCISES. 

1.  How  many  pints  in  9  quarts?  in  7  quarts? 

2.  In  14  pints  how  many  quarts  ? 

3.  In  8  bushels  how  many  pecks  ? 

4.  In  12  pecks  how  many  quarts  ? 

5.  In  32  quarts  how  many  pecks  ? 


MEASURE    OF   TIME. 


LESSON   XXII. 
MEASURE    OF   TIME. 


Time  is  the  measure  of  duration. 
The  Denominations  are  centuries,  years,  months, 
weeks,  days,  hours,  minutes,  and  seconds. 


TABLE. 

60  seconds  (sec.)  make  1  minute. 

60  minutes  make  1  hour. 

24  hours  make  1  day. 

7  days  make  1  week. 

4  weeks  and  2  days  or  }     ol     .,          .-• 
^  -.  J         >  make  1  montn. 

30  days  j 

make  1  year, 
make  1  year, 
make  1  year. 


365  days 

52  weeks 

12  calendar  months 
100  years 


make  1  century. 


mm. 

h. 

da. 

wk. 

mo. 


ycr: 


DIVISION    OF   THE   YEAH. 


Season.               Names  of  months. 

WintPr        j     l'  January> 
er>      }    2.  February, 

(    3.  March, 

Spring,       •]    4.  April, 

(    5.  May, 

6.  June, 

Summer, 

7.  July. 

8.  August, 

9.  September, 

Autumn, 

10.  October, 

11.  November, 

Winter,         12.  December. 

No.  of  days.        Abbreviations. 


31 

Jan. 

28  or  29 

Feb. 

31 

Mar. 

30 

Apr. 

31 

9 

30 

Jun. 

31 

—  , 

31 

Aug. 

30 

Sept. 

31 

Oct. 

30 

Nov. 

31 

Dec. 

365  or  366 

ROMAN    DOTATION. 


149 


LESSON   XXIII, 
TABLE  OF  ROMAN  NOTATION. 


I         denotes  one. 

XXX  denotes  thirty. 

II             u        two. 

XL          " 

forty. 

Ill           "        three. 

L             u 

fifty. 

IV           "        four. 

LX           " 

sixty. 

V             "        five. 

LXX 

seventy. 

VI           "        six. 

LXXX     " 

eighty. 

VII 

seven. 

XO           ' 

ninety. 

VIII 

eight. 

0 

one  hundred. 

IX 

nine. 

01 

one  hundred  one. 

X 

1        ten. 

CO            4 

two  hundred. 

XI 

4        eleven. 

coo 

three  hundred. 

XII 

1        twelve. 

COCO       4 

four  hundred. 

XIII 

4        thirteen. 

D               4 

five  hundred. 

XIV 

*        fourteen. 

DO 

six  hundred. 

XV           "        fifteen. 

DCO 

seven  hundred. 

XVI          "        sixteen. 

DCCO       4 

eight  hundred. 

XVII        "        seventeen. 

DCCOC    4 

nine  hundred. 

XVIII 

4        eighteen. 

M 

one  thousand. 

XIX 

4        nineteen. 

MD 

fifteen  hundred. 

XX 

4        twenty. 

MM           4 

two  thousand. 

XXI 

'        twenty-  one. 

X" 

ten  thousand. 

XXII 
XXIII 
XXIV 

4         twenty-two. 
u        t«-  enty-three 
"        twenty-four. 

M 

MM          " 

one  million, 
two  million. 

COUNTING. 


12  units  or  things  make  1 


12  dozen 
12  gross 
20  units 


dozen, 
gross. 

great  gross, 
score. 


PAPER. 

24  sheets  make  1  quire. 
20  quires      "       1  ream. 

2  reams      "       1  bundle. 

5  bundles  "       1  bale. 


150 


FEACTIONS. 


LESSON   XXIV. 
TABLE  OF  CIRCULAR  AND  ANGULAR  MEASURE. 

Circular  and  Angular  Measure  is  used  in 
measuring  the  arcs  of  circles  and  difference  of  direc- 
tions. 

The  Denominations  are  circles,  right-angles, 
quadrants,  signs,  degrees,  minutes,  and  seconds. 


60     seconds  (")  make     1 

60     minutes  make     1 

30     degrees  make     1 

degrees  make  -j 

quadrants  )          ,     J  1 

12  signs    f  make| 


90 


or 


minute. 

degree. 

sign.  sig. 

quadrant.         quad. 

right  angle.        r.  a. 

circumference 

or  circle. 


cir. 


FRACTIONS. 

LESSON   XXV. 


Two  halves.          Three  thirds.  Four  fourths.  Five  fifths. 

1.  How  many  halves  in  one  apple  ?  2  apples  ? 

2.  How  many  halves  in  one  peach?  3  peaches? 

3.  How  many  thirds  in  one  pie  ?  2  pies  ? 


One  half. 


One  third. 


Two  fourths. 


Three  fifths. 


1.  How  many  halves  make  one  melon?  2  melons? 

2.  How  many  thirds  make  one  pear?  2  pears? 

3.  How  many  fourths  make  one  orange  ?  2  oranges  ? 


FRACTIONS.  lol 

4.  What  is  meant  by  one-half  ?*  ANS.  One  of  the  two 
equal  parts  into  which  a  thing  or  a  number  of  things  is 
divided. 

'   5.  What  is  meant  by  one-third?  By  one-fifth?    By  one- 
seventh  *    By  one-eighth  ?     By  one-fourteenth  ? 

One.  1  half.  1  third.  1  fourth. 


6.  What  is  meant  by  two-thirds  ?  ANS.  Two  of  the  three 
equal  parts  into  which  a  thing  or  a  number  of  things  is 
divided. 

7.  What  is  meant  by  three-fourths  f  By  two-fifths?    By 
three-sevenths  ?    By  5   elevenths?     By   3    tenths?     By  3 
fifths  ? 

2  halves.  2  thirds.  3  fourths.  2  sixths. 


I  i       i  I        I       I  III 

2  fourths.  2  sixths.  3  fifths.  2  sevenths. 


I  "~   I        I  I     I     I     I     I  I     !     I      I  I     I      I     I     I     I 

8.  How  many  stars  in  1  half  of  six  stars  ?     In  1  third  of 
six  stars  ? 

1  half  of  six.  1  third  of  six. 


9.  How  many  apples  in  1  eighth  of  16  apples  ?     In  1  fifth 
of  10  apples  ?    In  1  third  of  15  pears? 

*N"OTK  FOK  THE  TEACHER.—  The  teacher  should  extend  the  illustrations 
in  fractions  on  the  blackboard,  and  by  oral  instruction  make  the  subject 
clear  to  the  class.  These  illustrations  are  only  suggestive  of  what  should  be 
done. 


152  SUMMARY. 

10.  How  many  are  1  third  of  6  nuts?     Of  12  oranges? 
Of  18  peaches?     Of  21  lemons? 
Fraction.     Name.          Fraction.      Name.          Fraction.       Name. 

i         1  half.    '         I-         1  sixth.  §  2  thirds.    ' 

£         1  third.  4         1  seventh.        J  3  fifths. 

J         1  fourth.        rV       1  tenth.  ^  5  twelfths. 

}        1  fifth.-  |         2  fourths.       &  7  twelfths. 

LESSON    XXVI. 
SUMMARY.* 

1.  Arithmetic  tells  about  numbers. 

2.  Notation  is  the  art  of  writing  numbers. 

3.  There  are  ten  figures  used  in  notation. 

4.  A  unit  is  one  of  any  kind  of  things. 

5.  Addition  is  finding  the  sum  of  two  or  more 
numbers. 

6.  Tha  answer  in  addition  is  called  the  sum. 

7.  Subtraction  is  taking  one  number  from    an- 
other to  find  the  difference. 

8.  The  minuend  is  the  number  to  be  subtracted 
from. 

9.  The   subtrahend  is  the   number  to  be  sub- 
tracted. 

10.  The  remainder  is  the  number  left  after  sub- 
tracting. 

11.  Multiplication  is  finding  the  product  of  two 
numbers. 


*NOTB  FOR  THE  TEACHER.— This  summary  should  be  first  discussed  by 
the  class  in  oral  lessons  before  being  committed  to  memory.  (See  Manual  of 
Arithmetic,  Sec.  II.) 


U.    8.    MONEY.  153 

12.  The  multiplicand  is  the  number  to  be  mul- 
tiplied. 

13.  The  multiplier  is  the  number  to  multiply 

by- 

14.  The  product  is  the  result  of  multiplication. 

15.  Division  is  finding  how  many  times  one  num- 
ber is  contained  in  another. 

16.  The  dividend  is  the  number  to  be  divided. 

17.  The  divisor  is  the  number  to  divide  by. 

18.  The  quotient  is  the  result  of  division. 

19.  The  remainder  is  the  part  of  the  dividend 
left  after  dividing. 

SIGNS. 

$     dollar  sign.         4  addition.          x  multiplication. 
=    equality.  —  subtraction,     -f-  division. 

LESSON   XXVII. 
UNITED  STATES  MONEY. 

The  Dollar  Sign  ($)  is  used  to  denote  dollars. 
The  Decimal  Point  ( . )  is  always  placed  between 
dollars  and  cents. 

TABLE  OF  ALIQUOT  PARTS. 

i  dol.  =  50  cts.  J  dol.  =  75  ots. 

I   "    =25  cts.  i  ct.  =  5  mills. 


154 


U.    8.    MONEY. 
REDUCTION  AND  ADDITION.* 

MODEL    OPERATIONS. 


$10    =  10.000 

114  cts. 

=$1.140 

3dol. 

=  3.000 

|ct. 

=  0.005 

Hit 

=  2.250 

3  mills-  0.003 

jdoL 

=     .750 

7ct, 

=  0.070 

$2.12£=  2.123 

21mills=  0.021 

$18.125 

ANS. 

• 

$1.239 

ANS. 

1.  Add        2 

.Add 

3.  Add 

4.  Add 

5.  Add 

6.  Add 

6  doll. 

$21 

$400 

$600 

4ct. 

$3 

3*    « 

$7* 

$17| 

$20 

13  ct. 

40  ct 

1    " 

m 

$200* 

$1 

*ct. 

25m. 

2*    " 

$40* 

$f 

$i 

2  m. 

$2* 

3f    " 

$25! 

$500£ 

If* 

7m. 

2*ct 

7.  Add        8.  Add 

9.  Add 

10.  Add      11.  Add 

12.  Add 

60  ct. 

34  m. 

50  ct. 

*  doll. 

|8| 

$3± 

25*  ct. 

12*  ct. 

25  doll. 

ict. 

3*ct. 

$30 

12*  ct. 

12*.  doll. 

12*  doll. 

10*  doll. 

5*  doll. 

f  doll. 

80  m. 

20  ct. 

12*ct. 

10*  ct. 

200  ct. 

*ct. 

46m. 

20m. 

60  m. 

300m. 

200  doll. 

500m. 

LESSON  XXVIII. 

SUBTRACTION. 

(a.)  From  $20  take  20  cts. 
(6.)  From  $2*  take  2*  cts. 


(c.y  From  f  doll,  take  *  ct. 
(d.)  From  $5|  take  50  mills. 


*  Before  leaving  the  subject  the  teacher  should  dictate  to  the  class,  at 
least,  ten  problems  similar  to  each  of  the  following. 

t  Fractions  should  in  every  case  he  changed  to  cents  and  mills. 


U.  S.  MONEY. 
MODEL  OPERATIONS. 


. 

$20.000  $2.500  $0.750  $5.750 

.200  .025  .005  .050 


$19.800  Axs.      $2.475  ANS.       $0.745  ANS.        $5.700  ANS. 

13.  From  $2  take  20  cts.     Take  99  cts. 

14.  From  $2£  take  25  cts.     Take  50  cts. 

15.  From  $100  take  100  cts.     Take  10  cts. 

16.  From  $40  J  take  40  cts.     Take  40  dol. 

17.  From  $200  take  200  cts.     Take  200  dol. 

18.  From  $25  take  25  cts.     Take  25  mills. 
10.  From  2£  dol.  take  2^  cts.     Take  2J  dol. 

20.  From  62|  cts.  take  12J-  cts.     Take  12  mills. 

21.  From  $18.90i  take  $l~.12i.     Take  5  mills. 

22.  From  $6  7  cts.  9  mills  take  $3.37£. 

23.  From  $5J  take  $1.62|.     Take  125~mil]s. 

24.  From  $1000  take  1000  cts.     Take  1000  mills. 

25.  From  |  dol.  take  £  ct.     Take  50  mills. 

LESSON   XXIX. 

MULTIPLICATION. 

(a.)  Multiply  $37|  by  4.     (b.)  Multiply  87{  ct.  by  33. 

MODEL    OPERATIONS, 
(a.)  (&.) 

$37.75  $0.875 

4  23 


$151.00  ANS.  2.625 

17.50 


$20.125  ANS. 


156  U.    S.    MONEY. 

26.  Multiply  $35|by  6,  by  11,  by  35,  by  108. 

27.  Multiply  $2.27  by  4,  by  12,  by  200,  by  207. 

28.  Multiply  $3.37*  by  11,  by  4,  by  306,  by  2002. 

29.  Multiply  $343  by  26,  by  37,  by  4007,  by  20. 

30.  Multiply  $4  312  by  6,  by  201,  by  38,  by  400. 
81.  Multiply  37^  cts.  by  16,  by  26,  by  106,  by  6006. 

32.  Multiply  2  cts.  7  mills  by  4,  by  24,  by  100,  by  3000. 

33.  Multiply  $2  2  m.  by  6,  by  5,  by  25,  by  37. 

34.  Multiply  3  dol.  3  cts.  3  mills  by  3,  by  4,  by  7,  by  10. 

35.  Multiply  8  dol.  8  mills  by  2,  by  22,  by  202,  by  10. 
86.  Multiply  3|  dol.  \  ct.  by  3,  by  303,  by  2,  by  8. 

LESSON    XXX. 

DIVISION. 

(a.)  Divide  $3  by  6.  (c.)  Divide  8  cts.  by  12. 

(6.)  Divide  $30^  by  20.       (<Z.)  Divide  $1.12|  by  12. 

MODEL    OPERATIONS. 

(a.)  (6.)  (c.)  «7.) 

6)  $3.000         20)  $30.500       12)  $0.080         12)  $1.125 


$0.500  ANS.        $1.525  ANS.    $0.006  +  *ANS.  $0.093  +  ANS. 

37.  Divide  $25  by  8,  by  5,  by  9,  by  12. 

38.  Divide  $30  by  11,  by  0,  by  9,  by  13. 

39.  Divide  $4|  by  9,  by  7,  by  11,  by  14. 

40.  Divide  $gj  by  7,  by  2,  by  4,  by  20. 

41.  Divide  $8.36  by  4,  by  2,  by  11,  by  7. 

42.  Divide  $1.121  by  3,  by  7,  by  9,  by  11. 

43.  Divide  87£  cts.  by  20,  by  37,  by  36,  by  28. 

44.  Divide  3  cts.  by  7,  by  11,  by  30,  by  25. 

*  NOTE. — The  sign  of  addition  placed  after  an  answer  shows  that  there  is 
t  remainder,  the  value  of  which  is  so  little  as  not  to  be  noticed. 


U.    8.    MONET. 


157 


45.  Divide  15  cts.  by  11,  by  30,  by  15,  by  150. 

How  many  times  are  12}  cts.  contained  in  $4?     In  $3f  ? 

MODEL    OPERATIONS. 

$0.125)  $4  OQO  (32  ANS.  $0.125)  $3.750  (30  ANS. 
375  375 


250  0 

250 

RULE.  —  Change  the  divisor  and  dividend  to  the  lowest 
denomination  found  in  either,  (if  not  so),  and  divide  as  in 
simple  division. 

46.  How  many  times  are  3  cts.  contained  in  $3  ?     In 
$3.33? 

47.  How  many  times  are  5|  cts.  contained  in  $5|?     In 
$203 | ? 

48.  How  many  times  are  20  cts.  contained  in  $20  ?     In. 
$2?     In  $5.20? 

49.  How  many  times  are  $1.12\  contained  in  $10.12J  ? 
In  $12.37^? 

50.  $4.40  are  how  many  times  4  cts.  ?     40  cts.  ?     5^  cts.  ? 

51.  $6J  are  how  many  times  25  cts.  ?     5  cts.  ?     9  cts.  ? 

LESSON  XXXI. 
APPLICATIONS  OF  U.  S.  MONEY.* 

52.  A  boy  bought  a  book  f  >r  $1,  a  slate  for  50  cts.  and  a 
sponge  for  12|  cts. ;  how  much  did  he  give  for  all  ? 

53.  A  lady  bought  some  calico  for  37J  cts.  and  some  lace 
for  $1 J ;   what  did  she  give  for  both  ? 

54.  A  boy  had  a  three  dollar  bill;   he-  paid  out  $1.37| ; 
how  much  had  he  left  ? 


*NOTE  FOR  THB  TEACH3R.—  The  formulas  to  be  used  in    the  solution 
of  these  problems  are  the  same  as  those  used  in  simple  numbers. 


158  U.    S.    MONEY. 

.55.  Lucy  bought  a  book  for  30  cts.,  an  inkstand  for  62f 
cts.,  and  some  paper  for  12  J  cts. ;  how  much  did  she  spend  ? 

56.  John  had  $11.37|,  he  gave  2 £  dollars  to  William- 
how  much  had  he  left  ? 

57.  A  boy  earned  $5J  in  a  week,  he  gave  his  father  $4|  • 
how  much  had  he  left? 

58.  A  boy  found  30  cts.*  he  then  earned  2£  dollars;  how 
much  had  he  then  ? 

59.  What  will  20  apples  coine  to  at  2  cts.  apiece  ?      At  3 
cts.  ?     At  2|  cts.  ? 

60.  If  the  interest  on  one  dollar  for  one  year  is  6  cts., 
what  is  the  interest  on  $347  ?     On  $276  ? 

61.  If  1  eighth  of  a  house  is  worth  $371.26,  what  is  8 
eighths  or  the  whole  house  worth  ? 

62.  A  man  gave  $387.27i   for  1  eighteenth  of  a  ship ; 
what  is  15  eighteenths  of  the  ship  worth? 

63.  One-sixth  of  a  church  cost  $1397.87| ;  what  did  5 
sixths  of  the  church  cost  ?     6  sixths  ? 

64.  One-ninth  of  a  factory  is  worth  $876.43  ;  what  is  5 
ninths  worth  ?    9  ninths,  or  the  whole  ? 

65.  Seven  boys  had  $12^  ;  how  much  is  that  apiece  ? 
FORM. — $12J  are  equal  to  12500  mills ;  if  7  boys  had  12500  mills, 

1  boy  must  have  1  seventh  of  12500  mills,  which  is  1785+  mills, 
or  $1.785. 

66.  If  9  boys  earned  $4J,  how  much  did  one  boy  earn? 
If  they  earned  $5  J  ?     $10.87^  ? 

67.  If  I  give  $1.37)1  for  a  book  how  much  will  16  copies 
cost  ?     27  copies  ?     1002  copies  ?     9070  copies. 

68.  If  one  pound  of  beef  costs  16^  cts.  how  much  will  3 
f  pounds  cost  ?     43" pounds  ?     307  pounds  ?     4003  pounds? 

69.  Seven  pounds  of  sugar  cost  $1.17  ?  how  much  is  that 
per  pound  ?    If  it  cost  $1.20  ?    If  it  cost  $1  J. 


U.    S.    MONEY.  159 

70.  Eight  pounds  of  cheese  cost  J-  of  a  dollar  ;  how  much 
was  that  a  pound  ?     If  it  cost  $1  £  I 

71.  I  have  a  dollar  bill  ;  how  many  oranges  can  I  buy 
with  it  at  5  cents  apiece  ?     At  2£  cts.  ? 

72.  How  many  pounds  of  beef  can  be  bought  for  $1.62J- 
at  12  1  cts.  per  pound  ? 

73.  How  many  oranges  can  be  bought  for  80  cents  at  5 
cts.  apiece  ?     At  2£  cts.  ? 

74.  How  many  pounds  of  rice  can  be  bought  for  $4.32, 
at  4  cts.  per  pound  ?     At  8  cts.  per  pound  ? 

75.  At  50  cts.  a  yard  how  many  yards  of  cloth  can  be 
bought  for  $12  ?     For  $16  ?     For  $18f 

76.  How  much  will  5  baskets  of  peaches  cost  at  $1.624 
per  basket  ?    At  $1.87^  ?    At  90£  cts.  ? 

77.  What  will  117  pounds  of  cheese  cost  at  16^  cts.  per 
pound.    At  12|  cts.?    At  11  cts.?     At  16  cts.? 

78.  What  must  I  give  for  1  yard  of  lace,  if  7  yards  cost 


79.  What  must  I  give  for  1   bushel  of  potatoes,  if  13 
bushels  cost  $8.90  ?     $4.37  ?     $11.87^  ?     $12  ? 

80.  What  will  1  pound  of  sugar  cost,  if  190  pounds  cost 
$30?     $35.50?     $27^  ?^  $33.33i? 

81.  What  must  I  pay  per  gallon  for  vinegar,  if  63  gallons 
or  a  hogshead  costs  $50  ?     $35  ? 

82.  A  boy  had  400  cts.,  he  gave  away  12£  cts.,  how  mucli 
had  he  left  ? 

83.  If  the  interest  on  one  dollar  for  a  year  is  5^  cts.,  how 
much  will  it  be  on  $20  ?     On  $75  ?     On  $375  ? 

84.  If  the  interest  on  one  dollar  for  a  year  is  7|  cts.,  how 
much  will  it  be  for  3  yrs.  ?     For  30  yrs  ? 

85.  If  the  interest  on  one  dollar  for  a  year  is  7?  cts., 
how  much  will  it  be  for  $3  ?     For  $2003  ? 


160  U.    S.    MONEY. 

86.  "What  will  12  pounds  of  pepper  cost  at  22  cts.  per 
pound?     At  19  cts.  ?     At  18  J  cts.  ?     At  $0.20.  ? 

87.  What  must  I  give  for  70  pounds  of  butter  at  37^  cts. 
per  pound  ?     At  50  cts.  ?     At  $0.40  J-  ? 

88.  What  must  be  given  for  200  pounds  of  pork  at  IS- 
cts.  per  pound?     At  12J-  cts.  ?     At  $0.22  ? 

89.  What  will  a  firkin  of  butter  be  worth  at  56  cts.  per 
pound  ?     At  37£  cts.  ?     At  $0.42  ? 

90.  What  will  a  barrel  of  flour  cost  at  8  cts.  per  pound? 
At  2|  cts.  ?    At  6  cts.  ?    At  0.07-J-  ? 

91.  What  must  I  give  for  a  barrel  of  beef  at  11  cts.  per 
pound.    At  9J  cts.  ?     At  $0.121 ;     At  13  cts.  ? 

92.  What  must  be  given  for  a  barrel  of  fish  at  12^  cts. 
per  pound?     At  8*  ?     At  $0.09  ?     At  $0.15 1  ? 

93.  What  will  a  barrel  of  salt  cost  at  2  cts.  per  pound  ? 
At  let.?    At  Jet.?    At  $0.01*? 

94.  What  will  a  bushel  of  oats  cost  at  2  cts.  per  pound  ? 
At  1|  cts  ?     At  $0.03^  ?     At  $0.02  £  ? 

95.  What  must  I  give  for  a  bushel  of  barley  at  2  cts.  per 
pound  ?     At  2i  cts.  ?     At  1*  cts. 

96.  What  must  be  given  for  a  bushel  of  wheat  at  3  cts. 
per  pound  ?     At  3£  cts.  ?     At  2£  cts^ 

97.  A  farmer  sold  a  bushel  of  rye  at  2 J-  cts.  per  pound ; 
how  much  did  he  receive? 

98.  A  man  bought  a  bushel  of  corn  for  $1.18  ;  how  much 
was  that  a  pound  ? 

99.  A  man  bought  a  bushel  of  rye  for  98  cts  ;  how  much 
was  that  per  pound  ? 

100.  A  man  bought  a  bushel  of  wheat  for  $2.25 ;  what 
was  that  per  pound  ? 

101.  How  many  pounds  in  3  firkins  of  butter  ?      In  9 
barrels  of  flour  ?  In  8  barrels  of  beef?     In  7  barrels  of  salt  ? 


ADDITION. 

• 

Ex.  1.  624   Ex. 

31.  73356   Ex. 

61.  157526 

2,  835 

32.  64377 

62.  182245 

3.  615 

330  73533 

63.  140513 

4.  636 

34.  71475 

64.  13112 

5.  713 

35.  62466 

65.  12213 

6.  316 

36.  7438 

66.  13122 

7.  634 

37.  10156 

67.  131130 

8.  726 

38.  7676 

68.  132110 

9.  725 

39.  99758 

69.  132421 

10.  4157 

40.  95668 

70.  134321 

11.  4247 

41.  8677 

71.  17455 

12.  7156 

42.  6667 

72.  14935 

13.  4446 

43.  8577 

73.  21496 

14.  6244 

44.  10256 

74.  16493 

15.  5155 

45.  9459 

75.  18564 

16.  6255 

46.  8377 

76.  18555 

17.  6266 

47.  8647 

77.  16166 

18.  72456 

48.  6496 

78.  17512 

19.  74665 

49.  8737 

79.  184254 

20.  72574 

50.  6988 

80.  198598 

21.  62865 

51.  18363 

81.  178467 

22.  736557 

52.  17283 

82.  206676 

23.  64854 

53.  15745 

83.  189305 

24.  56446 

54.  14425 

84.  172498 

25.  82286 

55.  164346 

85.  137085 

26.  155344 

56.  163475 

86.  203222 

27.  71376 

57.  17355 

87.  169785 

28.  85256 

58.  141722 

88.  189637 

29.  73575 

59.  142222 

89.  193052 

30.  32355 

60.  152651 

90.  151715 

162 


ANSWERS. 


91,  160254 

127.  285326 

163.  4871 

92.  17525 

128.  221632 

164.  286196 

93.  177205 

129.  238799 

165.  127166 

94  153731 

130.  253755 

166.  1612  c. 

95.  157^14 

131.  265712 

167.  211890 

96.  156683 

132.  186697 

168.  1996  a. 

97.  2120072 

133.  66256 

169.  2265  n. 

98.  189510 

134.  45546 

170.  222  c. 

99.  437591 

135.  88779 

171.  3140  c. 

100.  38019 

136.  249180 

172.  2686564 

101.  4698 

137.  192931 

173.  294395 

102.  51922 

138.  320105 

174.  269181 

103.  19388 

139.  217509 

175  303376 

104.  239065 

140.  276014 

176.  249409 

105.  19725 

141.  258123 

177  303737 

106.  17356 

142.  207811 

178  287065 

107.  23486 

143.  259626 

179.  3232393 

'.08.  158138 

144.  237775 

180/3465751 

109.  23182 

145.  232331 

181.  311175 

110.  22721 

146.  213276 

182.  34427 

111.  22105 

147.  215683 

183.  339700 

112.  241174 

148.  260014 

184.  277929 

113.  18340 

149  311730 

185.  304154 

114.  24411 

150.  146297 

186.  289039 

115.  224049 

151.  240553 

187.  289446 

116.  24298 

'  152.  32745 

188.  308648 

117.  16360 

153.  234941 

189.  285296 

118.  13975 

154.  21164 

190.  358489 

119.  20115 

155.  268399 

191.  302884 

120.  16823 

156.  209846 

192.  231950 

121.  19564 

157.  2634792 

193.  266875 

122.  20447 

158.  25869 

194.  368887 

123.  15107 

159.  242007 

195.  301027 

124.  200396 

160.  243015 

196.  232587 

125.  246121 

161.  172067 

197.  165775 

126.  226250 

162.  22700 

198.  211734 

SUBTRACTION. 


163 


199.  190280 

213.  283320 

227.  287647 

200.  22198 

214.  232451 

228.  2666  c. 

201.  203896 

215  26265 

229.  238  d. 

202.  3255- 

216.  273504 

230.  1402c. 

203.  3907 

217.  262512 

231.  222  o. 

204.  5121 

218.  25107 

232.  224  n. 

205.  3954 

219.  292550 

233.  1600d. 

206.  45121 

220.  241501 

234.  25141  c. 

207.  37293 

221.  206501 

235.  227  d. 

208.  4407 

222.  228469 

236.  309  q. 

209.  4063 

223  228232 

237.  30  c. 

210.  244729 

224.  285636 

238.  305  m. 

211.  243355 

225.  247645 

239.  3924  p. 

212.  240599 

226.  272617 

SUBTRACTION. 

Ex.  1.  6578 

Ex.  19.  2717    Ex.  37.  6823 

2.  2601 

20.  5864 

38.  8075 

3.  3023 

21.  2886 

39.  3026 

4.  2301 

22.  5902 

40.  .1030 

5.  3056 

23.  3176 

41.  765 

6.  10 

24.  5102 

42.  3126 

7.  2306 

25.  8076 

43.  7815 

8.  105 

26.  5412 

44.  3072 

9.  3056 

27.  8076 

45.  6573 

10.  2607 

28.  5431 

46.  2405 

11.  3056 

29.  3076 

47.  7902 

12.  3172 

30.  5723 

48.  1076 

13.  3023 

31.  7063 

49.  76175 

14.  5701 

32.  5601 

50.  30767 

15.  3026 

33.  8736 

51.  2683 

16.  3175 

34.  7573 

52.  8156 

17.  7607 

35.  3076 

53.  22084 

18.  5880 

36.  7905 

54.  20851 

164 


ANSWERS. 


55.  3146 

91.  60663 

127.  10400 

56.  5G122 

«92.  20002 

128.  50534 

57.  2045 

93.  36600 

129.  564 

58.  2084 

94.  71540 

130.  52000 

59.  2006 

95.  3500 

131.  20455 

60.  50643 

96.  65401 

132.  20400 

61.  25066 

97.  31410 

133.  46440 

62,  2001 

98.  66141 

134.  4044 

63.  8085  * 

99.  36000 

135.  60434 

64.  4203 

100.  10853 

136.  60533 

65.  7851 

101.  25468 

137.  20643 

66.  2945 

102.  31064 

138,  54300 

67.  6647 

103.  606453 

139.  46031 

68.  10000 

104.  64124 

140.  44540 

69.  4536 

105.  37001 

141.  57352 

70.  30452 

106.  205443 

142.  60834 

71.  65041 

107.  601 

143.  10470 

72.  86162 

108.  35002 

144.  50240 

73.  6562 

109.  46150 

145.  8043 

74.  70035 

110.  70046 

146.  5044 

75.  70023 

111.  10644 

147.  543 

76.  31563 

112.  21555 

148.  50444 

77.  25210 

113.  10606 

149,  25046 

78.  35001 

114.  36035 

150.  64413 

79.  21142 

115.  10032 

151.  5043 

80.  351 

116.  10205 

152.  33065 

81.  21575 

117.  36002 

153,  32042 

82.  20041 

118.  21444 

154.  504660 

83.  20113 

119.  20550 

155.  603 

84.  14120 

120.  60441 

156.  35041 

85.  20151 

121.  64051 

157  50130 

86,  20151 

122.  36002 

158.  55000 

87.  20150 

123.  55054 

159.  60405 

88.  305532 

124.  16654 

160.  581949 

89.  10142 

125.  405 

161.  495829 

90.  53500 

126,  45045 

162.  383969 

SUBTRACTION, 


11)5 


163,  194959 

199.  39592839 

235.  389788 

164.  491978 

200.  56562929 

236.  290989 

165.  294928 

201.  48353918 

237.  478989 

166.  680929 

202.  29566939 

238.  489889 

167.  281939 

203.  49661958 

239.  479779 

168.  490909 

204.  47382539 

240.  G98999 

169.  492929 

205.  26879855 

241.  698989 

170.  391616 

206.  47498655 

242.  699999 

171.  261636 

207.  66548989 

243.  639999 

172.  293826 

208.  5796789 

244.  698999 

173.  183958 

209.  3797879 

245.  1 

174.  692649 

210.  3879688 

246.  1 

175.  67590719 

211.  4876789 

247.  1 

176.  47284726 

212.  3998999 

248.  1 

177.  8394817 

213.  6999999 

249.  1 

178.  58564918 

214.  3999999 

250.  291913 

179.  39463856 

215.  1989899 

251.  720032 

180.  57363707 

216.  6979798 

252.  750570 

181.  29471817 

217.  3989899 

.253.  9374 

182.  57280918 

218.  1979798 

254.  568656 

183.  27281918 

219.  3969697 

255.  384699 

184.  25482837 

220.  2959655 

256.  88965 

185.  59284938 

221.  189695 

257.  147812 

186.  7686947 

222.  298655 

258.  674915 

187.  17495858 

223.  297968 

259.  217941 

188.  27373928 

224.  299966 

260.  31528 

189.  17265819 

225.  276966 

261.  171740 

190.  56575917 

226.  99679 

262.  611556 

191.  17697847 

227.  67787 

263.  429658 

192.  49488769 

228.  167686 

264.  751458  " 

193.  29495659 

229.  165767 

265.  157177 

194.  66175658 

230.  178977 

266.  786385 

195.  38254709 

231.  197879 

267.  578295 

196.  18050909 

232.  267978 

268.  7785944 

197.  59562979 

233/378798 

269.  272431 

198.  34586939 

234.  267798 

270.  197988 

166 


ANSWERS. 


271. 

97961 

299. 

739677199 

327. 

41843002 

272. 

529145 

300. 

7689880 

328. 

19299991 

273. 

744773 

301. 

3828657797 

329. 

6689891 

274. 

258769 

302. 

204999260 

330. 

391349206 

275. 

249736 

303. 

20999944 

331. 

774  p. 

276. 

28773 

304. 

888578302 

332. 

660  y. 

277. 

628943 

305. 

329985511 

333. 

357s. 

27S. 

650537 

306. 

886988202 

334. 

60  d. 

279. 

503847 

307. 

4000636 

335. 

21  m. 

280. 

322229 

308. 

2959998 

836. 

66  c. 

281. 

199600 

309. 

299909100 

337. 

2c. 

282. 

299941 

310. 

199098993 

338. 

2  d.  10 

c. 

283. 

488002 

311. 

42999991 

339. 

4  d.,  1  c. 

284. 

191181 

312. 

87999598 

340. 

7c. 

285. 

311232 

313. 

2448765 

341. 

6c. 

286. 

530536 

314. 

80115861 

342. 

3c. 

287. 

6000996 

315. 

9999997 

343. 

166  d. 

288. 

400046 

316. 

3333333 

344. 

5d. 

289. 

699992 

317. 

1811111 

345. 

138m. 

290. 

441996 

318. 

1 

127m. 

291. 

276993 

319. 

48969897 

73m. 

292. 

174017 

320. 

109090909 

346. 

110  c. 

293. 

349556 

321. 

1026003 

347. 

80  p. 

294. 

460240 

322. 

90899099 

348. 

274m. 

295. 

370744651 

323. 

27988776 

349. 

88  r. 

296. 

896919230 

324. 

10656294 

350. 

24  r. 

297. 

499779994 

325. 

51070025 

351. 

384  ft. 

298. 

599999994 

326. 

418575382 

352. 

768  ft. 

MULTIPLICATION. 

Ex.  1.  260486   Ex.  5.  42868426  Ex.  9.  8260846 

2.  480286  6.  680864     10.  8260486 

3.  648246  7.  8824608    11.  608068 

4.  68242086  8.  6482460    12.  6802086 


MULTIPLICATION. 


1G7 


13..  68468408  E: 

49.  103306368   79.  80  c. 

14.  68284608 

50.  10303368    80.  1280  c. 

15.  60824686 

51.  10369362    81.  414  c. 

16.  806804 

52.  10363935    82.  520  f. 

17.  6084086 

53.  13630368    83.  1748  cor. 

18.  8406084 

54.  19603068    84.  20  t. 

19.  6084082 

55.  10336392    85.  24  f. 

20.  6084608 

56.  13036392    86.  24  f. 

21.  8608028 

57.  130363035   87.  1280  w. 

22.  6084086 

58.  136336392   88.  184  q. 

23.  8608246 

59.  163036302   89.  32  cor. 

24.  8460846 

60,  163036035   90.  80  w. 

25.  82460826 

61.  536L84      91.  757283566 

26.  6080408 

62.  165364936      1135925349 

27.  8604864 

63.  I  >538168       1514567132 

28.  846084 

64.  27131:961:       1893208915 

29.  680486 

65.  33481-981:    92.  957200648 

30.  6408604 

66.  13616536       1435800972 

31.  13690392 

67.  2536972       1914401296 

32.  10369068 

68.  16549616.      2393001620 

33.  10306902 

69.  6705372     93.  757283668 

34.  13030962 

70.  27053748      1135925502 

35.  1036038 

71.  1749956       1514567336 

36.  13093092 

72.  27156052      1893209170 

37.  10393062 

73.  3914596     94.  936743668 

38.  13069302 

74.  1383948        1405115502 

39.  1300395 

75.  16559056       1873487336 

40.  130369302 

76.  7693566934     2341859170 

41.  10363092 

11540350401  95.  74372008 

42.  10339362 

15387133868    111558012 

43.  10303392 

77.  17412693564    148744016 

44.  1029it)35 

26119040346    185930020 

45.  13030302 

34825387128  96.  757284028 

46,  13030335 

78.  8335668172     1135926042 

47.  19303935 

12503502258    1514568056 

48.  10393062 

1  6670536344    1893210070 

168 

ANSWERS. 

97.  85572846 

106. 

682744 

126.  14050239  - 

128359269 

1024116 

187653652 

171145692 

1365488 

23417065 

213932115 

1706860 

28100478 

98.  75724808 

107. 

690  6  p. 

127.  10272480 

113587212 

1035  p. 

13696640 

151449616 

138  p. 

17120800 

189312020 

1726  p. 

20544960 

99.  66840846 

108. 

648 

128.  14040927 

100261269 

972 

18721236 

133681692 

1296 

23401545 

167102115 

1621170 

28081654 

100.  8140  c. 

109. 

6086  d. 

129.  96048276 

1.2210  c. 

9129  d. 

128064368 

16280c. 

12172  d. 

160080460 

20350  c. 

15215  d. 

192096552 

101.  74172  c. 

110. 

22446364 

130.  62041311 

111258  c. 

111. 

204426384 

82721748 

148344  c. 

112. 

22311858 

103402185 

185430  c. 

113. 

•251344206 

124082622 

102.  774  d. 

114. 

25180824 

131.  91925616 

1161  d. 

115. 

225624804 

122567488 

1548  d. 

116. 

40720824 

153209360 

1935  d. 

117. 

22440804 

183851232 

103.  874  c. 

118. 

41376498 

132.  104012529 

1311  c. 

119. 

251810046 

138683372 

1748  c. 

120. 

22311852 

173354215 

2185  c. 

121. 

25120452 

208025058 

104.  687  h. 

122. 

22718478 

33.  146035026 

10311  3ds. 

123. 

29450220 

194713368 

13748  4ths. 

124. 

223118472 

243391710 

17185  5ths. 

125. 

112255929 

292070052 

105.  7484  ch. 

149674572 

134.  113593116 

1122612  c. 

187093215 

151457488 

14967c. 

224511858 

189321860 

18710  c. 

227186232 

MULTIPLICATION. 


169 


135.  119358126 

144.  16746968 

153.  38722896 

159144168 

20933710 

48403620 

198930200 

25120452 

58084344 

238716252 

29307194 

67765068 

136.  12704013 

145.  15873652 

154.  15872288 

16938684 

19842065 

19840360 

21173355 

23810478 

23808432 

25408026 

27778891 

27776504 

137.  9740163 

146.  39145684 

155.  16786872 

12986884 

48932105 

20983590 

16233605 

58718526 

25180308 

19480326 

68504947 

29377026 

138.  12702783 

147.  19487328 

156.  13678688 

16937044 

24359160 

17098360 

25405566 

29230992 

20518032 

2L171305 

34102824 

23937704 

13.1  9724896 

148.  1871336 

157.  356720136 

12966528 

2339170 

445900170 

19449792 

2807004 

535080204 

16208160 

3274838 

624260238 

140.  14967468 

149.  4058808 

158.  243156076 

18709335 

5073510 

303945095 

22451202 

6088212 

364734114 

26193069 

7102914 

425523133 

141.  19145376 

150.  17382696 

159.  6683336 

23931720 

21728370 

8354170 

28718064 

26074044 

10025004 

33504408 

30419718 

11695838 

142.  19914688 

151.  13961664 

160.  5230416 

24893360 

17452080 

6538020 

29872032 

20942496 

7845624 

34850704 

24432912 

9153228 

143.  14967452 

152.  14832172 

161.  16282732 

18709315 

18540215 

20353415 

22451178 

22248258 

24424098 

26193041 

25956301 

28494781 

170 

ANSWERS. 

162, 

16121648 

171.  2391890310 

180.  24480455 

20152060 

2870268372 

29376546 

24182472 

3348646434 

34272637  ' 

28212884 

3827024496 

39168728 

163. 

12281648 

172.  209173920 

181.  18903445 

15352060 

251008704 

22684134 

18422472 

292843488 

26464823 

21492884 

334678272 

30245512 

164. 

16122848 

173.  3417084015 

182.  209845065 

20153560 

.  4100500818 

251814078 

24184272 

4783917621 

293783091 

28214984 

5467334424 

335752104 

165. 

170543215 

174.  209300170 

183.  33545310 

204651858 

251160204 

40254372 

238760501 

293020238 

46963434 

272869144 

334880272 

53672496 

166. 

2351854320 

175.  19553350 

184  1920110 

2822225184 

23464020 

2304132 

3292596048 

27374690 

2688154 

3762966912 

31285360 

3072176 

167. 

18902082065 

176.  15020060 

185.  1517010 

22682498478 

18024072 

1820412 

26462914891 

21028084 

2123814 

30243331304 

24032096 

2427216 

168. 

20335620 

177.  2752280 

186.  20151455 

24402744 

3302736 

24181746 

28469868 

3853192 

28212037 

32536992 

4403648 

32242328 

169. 

433917035 

178.  15493355 

187.  15393205 

520700442 

18592026 

.18471846 

607483849 

21690697 

21550487 

694267256 

24789368 

24629128 

170. 

3391709320 

179.  15109580 

188.  201539305 

4070051184 

*18131496 

241847166 

474^393048 

21153412 

^82155027 

5426734912 

24175328 

322462888 

M  ULTIPLIC  ATION. 


171 


189. 

153995930 

198.  2280294 

207.  2091624 

184795116 

2660343 

2440228 

215594302 

3040392 

2788832 

246393488 

3420441 

3137436 

190. 

208070076 

199.  2046420 

208.  2510040 

242748422 

2387490 

2928380 

277426768 

2728560 

3346720 

312105114 

3069630 

3765060 

191. 

2462088 

200.  250020 

209.  2318472 

2872436 

291690 

2704884 

3282084 

333360 

3091296 

3693132 

375030 

3477708 

192. 

2044134 

201,  22807584 

210.  336  s. 

2384823 

26608848 

392  d. 

2725512 

30410112 

448  d. 

3066201 

34211376 

504  d. 

193. 

2092224 

202.  2478252 

211.  94  p. 

2440928 

2891294 

2610  c. 

2789632 

3304336 

752  c. 

3138336 

3717378- 

658  c 

194. 

1971744 

203.  1812588 

212,  3402  d. 

2300368 

2114686 

224  d. 

2628992 

2416784 

3626  d. 

2957616 

2718882 

2237  d, 

195. 

1824372 

204.  2044032 

213.  126  h. 

2128434 

2384704  . 

126  f. 

2432496 

2725376 

504  f. 

2736558 

3066048 

252  th. 

196. 

2044608 

205.  26222538 

214.  1320  p. 

2385376 

30592961 

11880  1. 

2726144 

34963384 

95040  w. 

3066912 

39333807 

475200  1. 

197. 

2632236 

206.  41044254 

215.  296  c. 

3070942 

47884963 

414  c. 

3509648 

54725672 

710  c. 

3948354 

61566381 

118  c. 

172 


ANSWERS. 


216.  222  c. 
368  c. 
590  c. 
146  c. 

217.  33066924 
36073008 
390T9092 
42085176 

218.  50813178 
54721884 
58630590 
62539296 

219.  62974605 
67172912 
71371219 
75569526 

220.  71178711 
75365694 
79552677 
83739660 

221.  77703882 
81793560 
85883238 
89972916 

222.  87844596 
92027672 
96210748 
100393824 

223.  11461981 
11960328 
12458675 
12957022 

224.  169585400 
176368816 
183152232 
189935648 


225.  113121198  234.  225978060 
117310872      230086752 
121500546      234195444 
125690220      238304136 

226.  109805977  235.  582824538 
113592390      592702920 
117378803      602581302 
121165216      612459684 

227.  145028726  236.  29473542 
149707072      29941376 
154385418      30409210 
159063764      30877044 

228.  1381638522  237.  2573872 
1423506356     2612288 
1465374190     2650704 
1507242024     2689120 

229.  1220374190  238.  3339414 
1255242024     3386448 
1290109858     3433482 
1324977692     3480516 

230.  52364208   239.  2780100 
53706880       2817168 
55049552       2854236 
56392224      2891304 

231.  180033862  240.  321598256 
184220696      325669120 
188407530      329739984 
192594364      333810848 

232.  102914584  241.  254881712 
105104256      257952576 
1 07293928      26 1 023440 
109483600      264094304 

233.  4547588247  242.  35557422 
4636756644     35966128 
4725925041     36374834 
4815093438     36783540 


A 


MULTIPLICATION.  ]  73 

243.  3470864    252.27872136  270.  752000  Ib. 

69417280      313561530  271.  72520  Ib. 

1041259200    2829021804  272.  76000  Ib. 

13883456000    21607863434  273.  13160  Ib. 

244.20653840   253.25118232  274.  252  in. 

247846080     154895764  275.  216  in. 

2891537600     862392632  276.  96  in. 

33046144000    13405763144  277.  54ft. 

245.377016057   254.37676718  278.  8640  rd. 

3770160570    46049322  279.  108ft. 

37701605700    2515967502  280.  5280  s. 

377016057000    15493503702  281.  7040  s. 

246.  4983904    255.9721920  282.  14080  s. 
54822944      58331520  283.  184  qt. 
503374304     1954105920  284.  148  gi. 
4988887904    19482727680  285.  966  pt. 

247.  9366838    256.16335144  286.  2224  qt. 
103035218     98010864  287.  1868  pt. 
946050638     1233303372  288.  22800  sec. 
9376204838    24829418880  289.  1440  mi. 

248.  29359281   257.8366934  290.  364  da. 
293592810     251008020  291.  2000. 
3229520910    1255040100  292.  98  bbl. 

32295209100    8400401736  293.  940  d. 

249. 16745752    258.  432  yd.  294.  2983  d. 

184203272   259.  4536  d.  295.  1677  d. 

1858778472  260.  101745  c.  296.  48199  r. 

16929955272  261.  1003  d.  297.  729601  d. 

250.48393365    262.  7665  da.  298.  13406111  d. 

483933650   263-  8760  da,  299.  7236  sq.  m. 

4887729865  264.  1260  da.  300.  658018  sq.m. 

53232701500  265.  960  f. 
251.13256052    266.  7(580  p. 

132560520   267.  6825  s. 

914667588   268.  5952  oz. 

22097838684  269.  32700  Ib. 


174 


ANSWERS. 


DIVISION. 


Bern. 

Hem 

fix  1. 

214321  Ex. 

36. 

1454364 

1 

1695086695 

3 

2, 

104231 

37. 

234533664 

1 

68. 

230390173 

3. 

121340 

38. 

53653436 

1 

153593448 

2 

4. 

212413 

39. 

24356435 

1 

115195086 

2 

5. 

231430 

40. 

3456435 

1 

69. 

209393218 

1 

6. 

214311 

41. 

24536645 

1 

139598812 

1 

7. 

1023243 

42. 

53453436 

1 

104696609 

1 

8. 

1032431 

43. 

45363789 

2 

70. 

208039170 

1 

9. 

313441 

44. 

6563346 

1 

138692780 

1 

10. 

31242330 

45. 

46536365 

1 

104019585 

1 

11. 

234143 

46. 

4566972 

71. 

31206862 

12. 

312143 

47. 

146355636 

1 

20804574 

2 

13. 

312234 

48. 

45366376 

2 

15603431 

14. 

134123 

49. 

14466365 

1 

72. 

16  o. 

15. 

1231421 

50. 

1322031 

2488  c. 

16. 

12243012 

51. 

7899669 

1 

622  c. 

17. 

1241243 

52. 

678978 

1 

73. 

2172  a. 

18. 

1213412 

53. 

175897 

1 

1448  p. 

19. 

2314412 

54. 

268977 

1 

1086  o. 

20. 

20304012 

55. 

1579877 

1 

74. 

173d. 

21. 

4030121 

56. 

15789699 

1 

248  d. 

22. 

1032124 

57. 

26567899 

1 

1588  d. 

23. 

4213421 

58. 

15789885 

1 

75. 

128  yd. 

24. 

1241321 

59. 

1789567 

1 

191  yd. 

25. 

312140 

60. 

17575857 

1654  yd. 

26. 

1404321 

61. 

1789778 

1 

76. 

961  pk. 

27. 

2130421 

62. 

67658967 

1 

1922  pk. 

28. 

3124132 

63. 

17589786 

1 

3844  pk. 

29. 

1311139 

64. 

17859592 

1 

77. 

33  qt. 

30. 

2123412 

65. 

2689687 

1 

99  qt. 

31. 

12412134 

66. 

1709033901 

1 

198  qt. 

32. 

21342142 

1139355934 

1 

78. 

918  Ib. 

33. 

312412341 

854516950 

3 

1836  Ib. 

34. 

12141243 

67. 

3390173391 

1 

3672  Ib. 

35. 

12064321 

2260115594 

1 

79, 

16  h. 

DIVISION. 


175 


80. 

Rem. 

48  h. 
288  h. 
81  ft. 
48ft. 

Rem.               Rem 

837342    3  101.  30505516. 
91.  1859335   1      20337010  2 
1239557         15252758 
929667    3      12202206  2 

87  fr. 

743734 

1 

102.  33917050 

1 

SI. 

23yd. 

92.  2050335 

1 

22611367 

92yd. 

1366890 

1 

16958525 

1 

276  yd. 

1025107 

3 

13566820 

1 

82. 

27  Ib. 

820134 

1 

103.  2093391 

1 

36  Ib. 

93.  209383 

1 

1395594 

1 

97  Ib. 

139589 

1046695 

3 

83. 

lift. 

104691 

3 

837356 

3 

33ft. 

83753 

2 

104.  13958944 

2 

66ft. 

94.  2433591 

1 

10469208 

2 

84. 

1839152 

1622394 

1 

8375366 

4 

1226101 

1 

1216795 

3 

6979472 

2 

919576 

973436 

3 

105.  12359547 

1 

735660 

4 

95.  33591857 

9269660 

2 

85. 

20838356 

1 

22394571 

1 

7415728 

2 

13892237 

2 

16795928 

2 

6179773 

4 

10419178 

1 

13436742 

4 

106.  13594580 

2 

8335342 

3 

96.  2089317 

10195935 

2 

86. 

3393391 

1 

1392878 

8156748 

2 

2262261 

1044658 

2 

6797290 

2 

1696695 

3 

835726 

4 

107.  1392894 

1 

1357356 

3 

97.  3391933 

1 

1044670 

3 

87. 

2839188 

2261289 

835736 

3 

1892792 

1695966 

3 

696447 

1 

1419594 

1356773 

2 

108.  1023600 

1135675 

1 

98.  2033933 

1 

767700 

88. 

2393447 

1355955 

2 

614160 

1595631 

1 

1016966 

3 

511800 

1196723 

2 

813573 

2 

109.  1395954 

2 

957378 

4 

99.  3351703 

1046966  • 

89. 

2083591 

1 

2234468 

2 

837572 

4 

1389061 

1675851 

2 

697977 

2 

1041795 

3 

1340681 

1 

110.  1239547 

1 

833436 

3 

100.  2339185 

929660 

2 

90. 

2093356 

1 

1559456 

2 

743728 

2 

1395571 

1169592 

2 

619773 

4 

1046678 

1 

935674 

111.  1359557 

1 

176 


ANSWERS. 


Rem 

Rem 

Ren 

1019668 

699344 

1 

4386323 

815734 

2 

582786 

5 

132. 

1017668 

1 

679778 

4 

122. 

1419144 

814134 

3 

112. 

1234687 

1 

1064358 

678445 

3 

926015 

2 

851486 

2 

581524 

5 

740812 

2 

709572 

133. 

927160 

1 

617343 

4 

123. 

1377352 

741728 

1 

113. 

13769288 

1033014 

618106 

5 

10326966 

826411 

1 

529805 

6 

8261572 

4 

688676 

134. 

7696510 

3 

6884644 

124. 

1082653 

2 

6157208 

3 

114. 

10236890 

811990 

1 

5131007 

1 

7677667 

2 

649592 

1 

4398006 

1 

6142134 

541326 

5 

135. 

1017708 

2 

5118445 

125. 

1266255 

814166 

4 

115. 

13567078 

949691 

1 

678472 

2 

10175308 

2 

759753 

581547 

5 

8140246 

4 

633127 

8 

136. 

7677160 

2 

6783539 

126. 

1402634 

6141728 

2 

116. 

1023474 

1 

1051950 

2 

5118107 

767605 

3 

841580 

2 

4386948 

6 

614084 

3 

701317 

137. 

22295008 

2 

511737 

1 

127. 

714248 

2 

17836006 

4 

117. 

1135893 

1 

535686 

2 

14863339 

851920 

428549 

1 

12740004 

6 

681536 

367124 

2 

138. 

15197254 

3 

567946 

4 

128. 

1193011 

2 

12157803 

4 

118. 

1369022 

2 

894758 

3 

10131503 

1 

1026767 

715807 

8684145 

4 

821413 

3 

596505 

5 

139. 

9920180 

3 

684511 

2 

129. 

10195160 

1 

7936144 

3 

119. 

1395689 

8156128 

1 

6613453 

5 

1046766 

3 

6796773 

8 

5668674 

5 

837413 

2 

5825805 

6 

140. 

9354669 

3 

697844 

3 

130. 

767586 

2 

7483735 

4 

120. 

1362561 

614069 

1 

6236446 

3 

1021920 

3 

511724 

2 

5345525 

4 

817536 

3 

438620 

6 

141. 

13696586 

681280 

3 

131. 

7676065 

1 

10957268 

4 

121. 

1165573- 

2 

6140852 

1 

9131057 

2 

874180 

1 

5117376 

5 

7826620 

4 

143. 


144. 


142.  8  pt. 

162  pt. 

324  pt. 

648  pt. 

13  Ib. 

39  Ib. 

117  Ib. 

234  Ib. 

12  t. 

84  t. 
-252-t. 

24  t. 
145.  324s. 

162  s. 

108s. 

216  s. 

64  d. 

128  d. 

192  d. 

256  d. 

56  yd. 

112  yd. 

168  yd. 

224  yd. 

148.  13  d. 
26  d. 
39  d. 
52  d. 

149.  57  c. 
114  o. 
171  c. 
228  c. 
162  Ib. 
216  Ib. 
324  Ib. 
378  Ib. 
721  d. 
1442  d. 
3605  d. 
5047  d. 

152.  1437  d. 


146. 


147. 


150. 


151. 


DIVISION. 

2874  d. 
4311  d. 

lleiu. 

177 

Hem. 

13456573  a 
11774501  5 

5748  d. 

163. 

7341812 

2 

153. 

2244  c. 

6118177 

5202  c. 

5244151 

5 

5478  c. 

4588632 

6 

4278  c. 

164. 

10604233 

4 

154. 

81413668 

2 

8836861 

3 

67844723 

4 

7574452 

5 

58152620 

2 

6627646 

1 

50883542 

6 

165. 

6682172 

4 

155. 

60483340 

2 

5568477 

2 

50402783 

4 

4772980 

4 

43202386 

4176358 

37802087 

6 

166. 

14074172 

4 

156. 

80200082 

11728477 

2 

66833401 

4 

10052980 

4 

57285772 

6 

8796358 

50125051 

2 

167. 

833417 

1 

157. 

8214120 

2 

694514 

2 

6845100 

2 

595298 

5867228 

6 

520885 

6 

5133825 

2 

168. 

815720 

3 

158. 

8261412 

4 

679767 

1 

6884510 

4 

582657 

4 

5901009 

1 

509825 

3 

5163383 

169. 

614128 

2 

159. 

806812 

1 

511773 

4 

672343 

3 

438663 

1 

576294 

3 

383830 

2 

504257 

5 

170. 

6140820 

2 

160. 

6141721 

2 

511735 

2 

5118101 

1 

438630 

2 

4386943 

6 

383801 

4 

3838575 

7 

171. 

6815720 

2 

161. 

8141366 

4 

5679767 

6784472 

2 

4868371 

5 

5815262 

4259825 

2 

5088354 

2 

172. 

6140432 

2 

162. 

18839202 

3 

5117027 

15699335 

3 

4386023 

1 

178 


ANSWERS. 


Rem 

Rem 

,               Rem 

"3837770 

2 

'  183. 

6180111 

4 

5739723   K 

1T3. 

814372 

2 

5297238 

4 

5022258 

3 

678643 

4 

4035083 

6 

4464229 

6 

581694 

4 

4120U74 

4 

194. 

5118114 

5U8982 

6 

184. 

6971813 

5 

4386954 

6 

174. 

8372060 

4 

5975840 

3 

3888585 

4 

6976717 

2 

5228860 

3 

3412076 

5980043 

3 

4647875 

8 

195. 

6728473 

4 

5232538 

185. 

6181070 

5767263 

1 

175. 

16782134 

5298060 

5046355 

2 

13985111 

4 

4635802  ' 

4 

4485649 

1 

11987238 

4 

4120713 

3 

196. 

51181003 

3 

10488833 

6 

186. 

6951446 

2 

43869431 

4 

176. 

6080802 

2 

5958382 

4 

38385752 

5 

5067335 

2 

5213584 

6 

34120669 

4343430 

2 

4634297 

5 

197. 

666779 

4 

3800501 

4 

187. 

8862680 

3 

573239 

5 

177. 

7130091 

1 

7596583 

2 

501584 

6 

5941742 

4 

6647010 

3 

4'45853 

1 

5092922 

2 

5908453 

6 

198. 

511810 

4 

4456307 

188. 

2564593 

2 

438694 

6 

178. 

14619356 

1 

2198222 

6 

383858 

12182796 

5 

1923445 

341207 

1 

10442397 

2 

1708617 

7 

199. 

5069794 

9137097 

5 

189. 

6081602 

3 

4345537 

5 

179. 

6978644 

5212802 

1 

3802345 

4 

5981694 

6 

4561201 

7 

3379862 

6 

5233983 

4054401 

6 

200, 

34130843 

5 

4652429 

3 

190. 

10531726 

2 

29255009 

180. 

678384 

9027194 

25598132 

7 

581472 

7898794 

6 

22753895 

8 

508788 

7021150 

8 

201. 

63359122 

452256 

191. 

16460905 

2 

54307818 

6 

181. 

81784 

2 

14109347 

3 

47519341 

4 

70100 

6 

12345679 

42239414 

6 

61338 

2 

10973936 

8 

202. 

20559464 

5 

54522 

8 

192. 

6346440 

2 

17622398 

3 

182. 

5130077 

5 

5439806 

15419598 

5 

4397209 

4 

4759830 

2 

13706309 

8 

3847558 

3 

4230960 

2 

203. 

164609136 

5 

3420051 

8 

193. 

6696344 

3 

141093545 

6 

DIVISION. 


179 


Eem. 

Hem. 

Pi  em. 

123456852 

5 

165162 

224. 

8765767 

25 

109739424 

5 

214. 

220331 

13 

8546623 

18 

204. 

152549260 

4 

209315 

2 

8338169 

9 

139836822 

199:347 

15 

8139641 

16 

129080143 

5 

190286 

10 

225. 

13878666 

35 

119860133 

2 

215. 

243048 

13563242 

25 

205. 

169802740 

2 

231474 

6 

13261837 

8 

155652511 

10 

220952 

16 

12973536 

17 

143679241 

9 

211346 

2 

226. 

10514631 

27 

133416438 

10 

216. 

194466 

10295576 

36 

206. 

3155344 

6 

185626 

14 

10085462 

46 

2912625 

9 

177555 

21 

9883753 

34 

2704581 

170157 

18 

227. 

14522434 

32 

2524275 

217. 

18539280 

3 

13994346 

4 

207. 

3392387 

2 

17733224 

11 

13270500 

34 

3131434 

4 

16994340 

3 

12828150 

34 

2907760 

6 

16314566 

13 

228. 

144P0098 

2 

2713909 

11 

218. 

12827674 

11 

13850829 

208.' 

3135108 

9 

12314567 

12 

13455091 

2 

2911172 

5 

11840930 

7 

12558084 

72 

2717094 

3 

11402377 

8 

229. 

1622540 

44 

2547275 

13 

219. 

16030027 

10 

1530350 

64 

209. 

2199029 

6 

15436322 

18 

1417588 

4 

2052427 

7 

14885025 

12 

1374192 

48 

1921150 

12 

14-171748 

20 

230. 

411194 

96 

1810965 

7 

220. 

14895836 

8 

373470 

72 

210. 

626973 

8 

14382186 

22 

194776 

118 

587787 

11 

13902780 

16 

19293 

72 

553211 

16 

13454303 

23 

231. 

15393 

43 

522477 

17 

221. 

11393880 

12 

14872 

139 

211. 

460026 

5 

11026335 

27 

14187 

64 

432377 

12 

10681762 

28 

10365 

238 

408912 

5 

10358073 

3 

232. 

13524 

140 

382127 

8 

222. 

10680725 

15 

13217 

28 

212. 

316745 

6 

10357067 

4 

12373 

147 

299148 

7 

10052447 

17 

10464 

368 

283403 

14 

9765234 

25 

233. 

62038 

122 

269233 

11 

223. 

14223612 

7 

69704 

132 

213. 

198244 

10 

13828511 

31 

C5790 

10 

182547 

9 

13454768 

11 

63725 

230 

173420 

2 

13100695 

17 

234. 

8140 

340 

180 


ANSWERS. 


Bern. 

Item. 

Bern 

7565 

370 

102361 

12 

81       1650 

8028 

144 

3070 

842 

255. 

4194  d. 

7636 

352 

•245. 

100767 

22 

3816  d. 

235. 

4678 

384 

80614 

2 

3240  d. 

4574 

414 

67178 

22 

2240  d 

5053 

481 

1007 

2702 

256. 

494  c. 

4940 

364 

246. 

16268 

3 

2082  c. 

236. 

4852 

55 

5810 

3 

3123  c. 

5491 

580 

5083 

63 

2776  c. 

5099 

433 

81 

1298 

257. 

245  d. 

5182 

497 

247. 

102362 

4 

702  d. 

237. 

4437 

143 

34120 

64 

7809  d. 

4552 

400 

40406 

8 

258. 

46ft. 

4100 

716 

506 

4504 

259. 

92  ft. 

4292 

172 

248. 

94652 

5 

260. 

366  rd. 

238. 

4364 

234 

60746 

59 

261. 

1360  rd. 

4410 

174 

49036 

53 

262. 

1487  yd. 

4328 

170 

580 

5981 

263. 

374  mi. 

4457 

94 

249. 

11995 

29 

264. 

196  mi. 

239. 

4379 

185 

6982 

40 

265. 

54  rd. 

4826 

57 

4976 

90 

266. 

1145  ft. 

5539 

504 

57 

7274 

267. 

1721  d. 

9365 

181 

250. 

19957 

7 

268. 

25  yd. 

240. 

7084 

142 

16782 

8 

269. 

4082  d. 

9469 

507 

11021 

9 

270. 

582  c. 

15891 

197 

144 

4160 

271. 

160  c. 

21136 

218 

251. 

12667 

11 

272. 

996  d. 

241. 

2043 

532 

72836 

2 

273. 

1748  d. 

2154 

316 

30139 

3 

274. 

10  d. 

3478 

148 

223 

2773 

275. 

271  bu. 

4566 

340 

252. 

7066 

52 

276. 

388  bu. 

242. 

6140 

147 

6173 

17 

277. 

820  d. 

4793 

396 

5653 

33 

278. 

292  c. 

6786 

327 

63 

7490 

63  c. 

12543 

103 

253. 

7152 

16 

156  c. 

243. 

47335 

54 

8046 

16 

279. 

169  c. 

59865 

44 

9195 

49 

972  o. 

40708 

64 

78 

5362 

925  c. 

4066 

798 

254. 

4663 

48 

280. 

150001, 

244. 

307084 
153542 

2 
2 

5596 
6995 

26 
26 

281. 
282. 

142  c. 
753  Ib. 

U.  6.  MONEY. 


181 


283.  18825  Ib 

284.  8  c. 


1.  $15.50 

2.  $97.50 

3.  $1119.25 

4.  $622.25 

5.  $0.184 

6.  $5.95 

7.  $1.006 

8.  $12.879 

9.  $38.185 

10.  $11.41 

11.  $211.285 

12.  $34.505 

13.  $1.80 
$1.01 

14.  $2.25 
$2 

15.  $99 
$99.90 

16.  $40.35 
$0.75 

17.  $198;— 

18.  $24.75 
$24.975 

19.  $2.475;— 

20.  $0.50 
$0.613 

21.  $17.78 
$18.90 

22.  $2.704 

23.  $4.125 
$5.625 

24.  $990 


25.  $0.495 

$0.45 


285.  2  d, 

287.  4  c. 

286.  5  c. 

288,  6992  Ib. 

U.  S.  MONEY. 

26.  $213 

35.  $16.016 

$390.50 

$176.176 

$1242.50 

$1617.616 

$3834 

$80.08 

27.  $9.08 

36.  $11.265 

$27.24 

$1137.765 

$454 

$7.51 

$469.89 

$30.04 

28.  $37.125 

37.  $3.125 

$13.50 

$5 

$1032.75 

$2.777  + 

$6756.75 

$2.083  + 

29.  $97.50 

38.  $2727  + 

$138.75 

$5 

$15026.25 

$3.333  + 

$75 

$2.307  + 

SO.  $25.872 

39.  $0.50 

$1866.712 

$0.642  + 

$163.856 

$0.409  + 

$1724.80 

$0321  + 

31.  $6;  $9.75 

40.  $0535  + 

$39.75 

$1875  + 

$2252.25 

$0.937  + 

32.  $0.108 

$0.187  + 

'$0.648 

41.  $2.09 

$2.70 

$4.18 

$81 

$0.76 

33.  $12.012 

$1.194  + 

$10.01 

42.  $0.375 

$50.05 

$0.160  + 

$74.074 

$0.125 

34.  $3.099 

$0.102  + 

$12.132 

43.  $0.043  + 

$21.231 

$0.023  + 

$30.33 

$0.0-24  + 

QA 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


BY 

CHARLES  SCRIBNER  &  CO. 


GEOGRAPHY. 

if,  Arnold  Guyot's  Introduction  to  the  Study  of  Geography. 
Jrof.  Arnold  Guyot's  Elementary  Geography  for  Primary  Classes, 
Prof.  Arnold  Guyot's  Intermediate  Geography. 
Prof.  Arnold  Guyot's  Common  School  Geography. 
Prof.  Arnold  Guyot's  Common  School  Gecgrapny,  Teachers'  Edition. 
Prof.  Arnold  Guyot's  Wall  Maps  (two  sizes)  of  tne  United  State*. 
Prof,  Arnold  Guyot's  Wall  Maps  (two  sizes)  Of  North  America. 
Prof.  Arnold  Guyot's  Wall  Maps  (two  sizes)  Of  South  America- 
Prof.  Arnoid  Guyot's  Wall  Maps  (two  sizes)  of  Europe. 
Prof.  Arnold  ikjetfi  Wall  Maps  (two  sizes)  of  Asia. 
Prof.  Arnold  Guyoi  &  Wall  Maps  (two  sizes)  of  Africa. 
Prof.  Arnold  Guyot's  W. '!  Maps  of  Central  Europe. 
Prof.  Arnold  Guyot's  Wall  Xapa  of  Australia. 
Prof.  Arnold  Guyot's  Popular  Portfolio  Wall  Maps.  $18  per  Sot  of 
Prof,  Arnold  Guyot's  Key  to  the  Well  Maps.  [ten  Maps. 

GLOBES. 

Perce's  Magnetic  Globes,  eight  styles  and  sizeb,  varying  in  price  from 

|  $5  to  $85. 
ARITHMETIC. 

Felter's  Natural  Series. 
COMPOSITION. 


Prof.  Henry  N,  Day's  Art  of  English  Composition. 
Prof.  Henry  N.  Day's  Art  of  Discourse. 
Prof.  Henry  N.  Day's  Elements  of  Logic. 

NATURAL,    HISTORY. 

Prof.  Sanborn  Tenney's  Manual  of  Zoology,  profusely  illustrated. 
Prof.  Sanborn  Tenney's  Manual  of  Zoology,  (Lib.  Ed.)     " 
Prof.  Sanborn  Tenney's  Natural  History  of  Animals.      " 
Prof.  Sanborn  Tenney's  Natural  History  Tablets, 

OBJECT-TEACHING. 

Prof.  E.  A.  Sheldon's  Elementary  Instruction. 
Prof.  E.  A.  Sheldon's  Lessons  on  Objects. 
Prof.  E.  A.  Sheldon's  First  Reading-Book. 
Prof.  E.  A.  Sheldon's  Phonic  Reading  Charts. 

ggg-  Descriptive  Catalogue,  with  Price-List,  forwarded  free  of 
postage  to  any  address.  Most  favorable  terms  afforded  to  Teachers 
desiring  to  procure  the  above  Text-Books  for  examination.  Special 
terms  made  for  first  introduction. 

CHARLES  SCRIBNER  &  CO., 

PUBLISHERS,  654  Broadway,  New  York. 


